Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems.
MatLab is a matrix-based program used for numeric computation and visualization. It contains functions for creating matrices and performing operations on them like addition, subtraction, multiplication, etc. It also allows plotting of functions and special matrices like magic squares, identity matrices, and Toeplitz matrices. Polynomial operations can also be performed such as addition, multiplication, differentiation and evaluation.
This document provides an introduction and overview of MATLAB (Matrix Laboratory), an interactive program for numerical computation and visualization. It discusses basic MATLAB commands and functions for creating variables and matrices, performing mathematical operations, plotting graphs, and working with polynomials.
Here are the steps to solve this problem numerically in MATLAB:
1. Define the 2nd order ODE for the pendulum as two first order equations:
y1' = y2
y2' = -sin(y1)
2. Create an M-file function pendulum.m that returns the right hand side:
function dy = pendulum(t,y)
dy = [y(2); -sin(y(1))];
end
3. Use an ODE solver like ode45 to integrate from t=0 to t=6pi with initial conditions y1(0)=pi, y2(0)=0:
[t,y] = ode45
This document provides a cheat sheet for common Matlab commands and functions. It summarizes basics like saving/loading variables, constructing matrices, defining variables, arithmetic operations, solving equations, plotting, and transposes/dot products. Key commands include save, load, rand, zeros, ones, eye, diag, sin, plot, eig, and dot for constructing matrices, numerical operations, solving equations, plotting, and linear algebra.
This document discusses creating and manipulating arrays in MATLAB. It covers:
- Creating one-dimensional arrays (vectors) using known values, spacing, or number of elements.
- Creating two-dimensional arrays (matrices) by specifying rows and ensuring each row has the same number of columns.
- Basic array commands like zeros, ones, and eye to create arrays filled with zeros, ones, or an identity matrix.
- Transposing arrays with the ' operator.
- Accessing and assigning values to individual elements or ranges of elements using indexing and colon notation.
- Adding elements to existing arrays by assigning values to undefined indices or appending rows/columns.
The document discusses various topics related to graphics and plotting in MATLAB including: the plot command for creating 2D and 3D plots; options for specifying line styles; using linspace to generate uniformly spaced vectors; adding labels, titles, and text to figures; displaying data using plots, stem plots, bar charts; and including multiple graphs in the same figure. Key graphing functions covered are plot, stem, bar, title, xlabel, ylabel, text, and linspace. The document also includes examples of MATLAB code for generating various types of graphs and annotating them.
This document provides an introduction and overview of MATLAB. It defines MATLAB as an interactive system for technical computing with matrices as the basic data type. It describes how MATLAB is used in mathematics, industry, and research for numeric computation and visualization. The document outlines MATLAB's toolboxes for specialized applications and provides examples of using matrices, vectors, operators, and functions in MATLAB. It demonstrates how to perform operations like matrix addition and inversion, solve systems of linear equations, and analyze arrays with built-in functions.
The document discusses various raster algorithms including raster displays, monitor intensities, RGB colour, line drawing, and simple anti-aliasing. It provides details on how raster displays work by representing images as a grid of pixels stored in a frame buffer and scanned line by line on the screen. It also describes how monitor intensities are represented digitally and processed, the RGB color model, algorithms for line drawing including DDA and Bresenham's, and different methods for simple anti-aliasing like supersampling.
MatLab is a matrix-based program used for numeric computation and visualization. It contains functions for creating matrices and performing operations on them like addition, subtraction, multiplication, etc. It also allows plotting of functions and special matrices like magic squares, identity matrices, and Toeplitz matrices. Polynomial operations can also be performed such as addition, multiplication, differentiation and evaluation.
This document provides an introduction and overview of MATLAB (Matrix Laboratory), an interactive program for numerical computation and visualization. It discusses basic MATLAB commands and functions for creating variables and matrices, performing mathematical operations, plotting graphs, and working with polynomials.
Here are the steps to solve this problem numerically in MATLAB:
1. Define the 2nd order ODE for the pendulum as two first order equations:
y1' = y2
y2' = -sin(y1)
2. Create an M-file function pendulum.m that returns the right hand side:
function dy = pendulum(t,y)
dy = [y(2); -sin(y(1))];
end
3. Use an ODE solver like ode45 to integrate from t=0 to t=6pi with initial conditions y1(0)=pi, y2(0)=0:
[t,y] = ode45
This document provides a cheat sheet for common Matlab commands and functions. It summarizes basics like saving/loading variables, constructing matrices, defining variables, arithmetic operations, solving equations, plotting, and transposes/dot products. Key commands include save, load, rand, zeros, ones, eye, diag, sin, plot, eig, and dot for constructing matrices, numerical operations, solving equations, plotting, and linear algebra.
This document discusses creating and manipulating arrays in MATLAB. It covers:
- Creating one-dimensional arrays (vectors) using known values, spacing, or number of elements.
- Creating two-dimensional arrays (matrices) by specifying rows and ensuring each row has the same number of columns.
- Basic array commands like zeros, ones, and eye to create arrays filled with zeros, ones, or an identity matrix.
- Transposing arrays with the ' operator.
- Accessing and assigning values to individual elements or ranges of elements using indexing and colon notation.
- Adding elements to existing arrays by assigning values to undefined indices or appending rows/columns.
The document discusses various topics related to graphics and plotting in MATLAB including: the plot command for creating 2D and 3D plots; options for specifying line styles; using linspace to generate uniformly spaced vectors; adding labels, titles, and text to figures; displaying data using plots, stem plots, bar charts; and including multiple graphs in the same figure. Key graphing functions covered are plot, stem, bar, title, xlabel, ylabel, text, and linspace. The document also includes examples of MATLAB code for generating various types of graphs and annotating them.
This document provides an introduction and overview of MATLAB. It defines MATLAB as an interactive system for technical computing with matrices as the basic data type. It describes how MATLAB is used in mathematics, industry, and research for numeric computation and visualization. The document outlines MATLAB's toolboxes for specialized applications and provides examples of using matrices, vectors, operators, and functions in MATLAB. It demonstrates how to perform operations like matrix addition and inversion, solve systems of linear equations, and analyze arrays with built-in functions.
The document discusses various raster algorithms including raster displays, monitor intensities, RGB colour, line drawing, and simple anti-aliasing. It provides details on how raster displays work by representing images as a grid of pixels stored in a frame buffer and scanned line by line on the screen. It also describes how monitor intensities are represented digitally and processed, the RGB color model, algorithms for line drawing including DDA and Bresenham's, and different methods for simple anti-aliasing like supersampling.
This document provides an introduction to MATLAB. It discusses that MATLAB is a high-level language for technical computing where everything is a matrix and it is easy to perform linear algebra. It describes the MATLAB desktop interface and valid variable names. It also summarizes how to perform basic operations like addition, subtraction, multiplication, etc. on matrices and vectors. Finally, it outlines various matrix operations, statistical functions, random number generation, and plotting in MATLAB.
MATLAB is a programming tool that simplifies programming compared to languages like C and C#. The document introduces basic MATLAB functions like help, inputting matrices and vectors, matrix operations, loops, conditional statements, and graphs. It also covers symbolic math, Laplace transforms, Fourier transforms, and other domains and transforms. The overall document serves as an introduction to essential MATLAB programming concepts and capabilities.
This document provides a cheat sheet summarizing common Matlab commands for defining and manipulating variables, performing arithmetic operations on numbers and matrices, plotting functions, and solving linear equations. Key commands include save and load to save and load variables, whos to list variables, clear to delete variables, and help/doc for command documentation. It also covers defining matrices and vectors, element-wise and matrix operations, transposes, constructing matrices, extracting portions of matrices and vectors, and plotting functions.
The document provides an assessment review with multiple choice questions about math concepts like algebra, geometry, and coordinate planes. It includes 15 questions testing skills like simplifying expressions, solving equations, factoring polynomials, and graphing lines. The questions are formatted with explanations of steps required to arrive at the answers.
This document provides an introduction to MATLAB. It covers MATLAB basics like arithmetic, variables, vectors, matrices and built-in functions. It also discusses plotting graphs, programming in MATLAB by creating functions and scripts, and solving systems of linear equations. The document is compiled by Endalkachew Teshome from the Department of Mathematics at AMU for teaching MATLAB.
This document provides solutions to 21 problems involving vector and matrix operations in MATLAB. Some key problems include:
- Calculating values of functions for given inputs using element-by-element operations
- Finding the length, unit vector, and angle between vectors
- Performing operations like addition, multiplication, exponentiation on vectors and using vectors in expressions
- Computing the center of mass and verifying vector identities
- Solving physics problems involving projectile motion using vector components
This document provides an overview of MATLAB, including:
- MATLAB is a software package for numerical computation, originally designed for linear algebra problems using matrices. It has since expanded to include other scientific computations.
- MATLAB treats all variables as matrices and supports various matrix operations like addition, multiplication, element-wise operations, and matrix manipulation functions.
- MATLAB allows plotting of 2D and 3D graphics, importing/exporting of data from files and Excel, and includes flow control statements like if/else, for loops, and while loops to structure code execution.
- Efficient MATLAB programming involves using built-in functions instead of custom functions, preallocating arrays, and avoiding nested loops where possible through matrix operations.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
The document discusses arrays and array data structures. It defines an array as a set of index-value pairs where each index maps to a single value. It then describes the common array abstract data type (ADT) with methods like create, retrieve, and store for manipulating arrays. The document also discusses sparse matrix data structures and provides an ADT for sparse matrices with methods like create, transpose, add, and multiply.
1. The document provides examples of various functions in R including string functions, mathematical functions, statistical probability functions and other statistical functions. Examples are given for functions like substr, grep, sub, paste etc. to manipulate strings and functions like mean, sd, median etc. for statistical calculations.
2. Examples are shown for commonly used probability distribution functions like dnorm, pnorm, qnorm, rnorm etc. Other examples include functions for binomial, Poisson and uniform distributions.
3. The document also lists various other useful statistical functions like range, sum, diff, min, max etc. with examples. Examples are provided to illustrate the use of these functions through loops and to create a matrix.
This document provides an overview of basic MATLAB concepts including:
1. Creating variables and performing basic arithmetic operations
2. Generating and manipulating matrices using built-in functions
3. Plotting graphs of simple functions like sine and cosine waves
4. Solving linear equations and finding the inverse and determinant of matrices
It includes sample exercises demonstrating these MATLAB skills.
1. The document discusses matrices and various matrix operations.
2. It defines what a matrix is and different types of matrices such as row matrix, column matrix, square matrix, diagonal matrix, triangular matrix, and null matrix.
3. It covers matrix addition and multiplication. Matrix addition involves adding corresponding elements of two matrices of the same size. Matrix multiplication is only defined if the number of columns of the first matrix equals the number of rows of the second matrix.
1) Matrices can be defined as row vectors, column vectors, or 2D matrices in MATLAB. Common operations include addition, subtraction, multiplication, and exponentiation.
2) Predefined functions like ones, zeros, eye, and rand can be used to create matrices. Other functions like sum, diag, transpose, inv, and det perform operations on matrices.
3) Matrices can be concatenated horizontally using [A B] or vertically using [A;B]. Elements can be indexed and extracted from matrices using normal, linear, or logical indexing.
This document provides an overview of MATLAB, including its common uses in engineering fields like rocket design, its basic commands and functions for mathematics, matrices, polynomials, and more. Key features of MATLAB covered include its command window, editor, predefined math functions, matrix commands using colons, reading and writing files, and basic programming statements.
This document provides an overview of plotting functions in MATLAB. It discusses how to generate basic and 3D plots, customize plots using options like color, style and labels, and control the plot appearance using functions such as axis, title, legend. Examples are given to illustrate plotting a simple function, holding multiple plots, using subplots, and generating surface plots. The document also covers plotting in 3D using functions like surf, plot3 and manipulating axes properties.
This document provides contact information for math assignment help, including a phone number and email address. It then presents solutions to several problems from a linear algebra textbook. The problems cover topics like writing a quadratic form as a sum of squares, finding the closest line and plane of best fit to a set of points, orthonormal vectors, and determinants. Solutions are provided in mathematical notation and include working steps.
The document defines matrices and their properties, including symmetric, skew-symmetric, and determinant. It provides examples of solving systems of equations using matrices and their inverses. It also discusses properties of determinants, including properties related to symmetric and skew-symmetric matrices. Inverse trigonometric functions are defined, including their domains, ranges, and relationships between inverse functions using addition and subtraction formulas. Sample problems are provided to solve systems of equations and evaluate determinants.
This document contains a 45 item multiple choice test on additional mathematics. It provides instructions for taking the test, including that it has 45 items to be completed in 1 hour and 30 minutes. It also lists some formulae provided on page 2. Each item has 4 answer choices labeled A, B, C, or D. Students are to record their answers on an answer sheet by shading the corresponding space for the choice they believe is best. A sample item is worked through as an example. Calculators may be used.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
This document provides an introduction to MATLAB. It discusses that MATLAB is a high-level language for technical computing where everything is a matrix and it is easy to perform linear algebra. It describes the MATLAB desktop interface and valid variable names. It also summarizes how to perform basic operations like addition, subtraction, multiplication, etc. on matrices and vectors. Finally, it outlines various matrix operations, statistical functions, random number generation, and plotting in MATLAB.
MATLAB is a programming tool that simplifies programming compared to languages like C and C#. The document introduces basic MATLAB functions like help, inputting matrices and vectors, matrix operations, loops, conditional statements, and graphs. It also covers symbolic math, Laplace transforms, Fourier transforms, and other domains and transforms. The overall document serves as an introduction to essential MATLAB programming concepts and capabilities.
This document provides a cheat sheet summarizing common Matlab commands for defining and manipulating variables, performing arithmetic operations on numbers and matrices, plotting functions, and solving linear equations. Key commands include save and load to save and load variables, whos to list variables, clear to delete variables, and help/doc for command documentation. It also covers defining matrices and vectors, element-wise and matrix operations, transposes, constructing matrices, extracting portions of matrices and vectors, and plotting functions.
The document provides an assessment review with multiple choice questions about math concepts like algebra, geometry, and coordinate planes. It includes 15 questions testing skills like simplifying expressions, solving equations, factoring polynomials, and graphing lines. The questions are formatted with explanations of steps required to arrive at the answers.
This document provides an introduction to MATLAB. It covers MATLAB basics like arithmetic, variables, vectors, matrices and built-in functions. It also discusses plotting graphs, programming in MATLAB by creating functions and scripts, and solving systems of linear equations. The document is compiled by Endalkachew Teshome from the Department of Mathematics at AMU for teaching MATLAB.
This document provides solutions to 21 problems involving vector and matrix operations in MATLAB. Some key problems include:
- Calculating values of functions for given inputs using element-by-element operations
- Finding the length, unit vector, and angle between vectors
- Performing operations like addition, multiplication, exponentiation on vectors and using vectors in expressions
- Computing the center of mass and verifying vector identities
- Solving physics problems involving projectile motion using vector components
This document provides an overview of MATLAB, including:
- MATLAB is a software package for numerical computation, originally designed for linear algebra problems using matrices. It has since expanded to include other scientific computations.
- MATLAB treats all variables as matrices and supports various matrix operations like addition, multiplication, element-wise operations, and matrix manipulation functions.
- MATLAB allows plotting of 2D and 3D graphics, importing/exporting of data from files and Excel, and includes flow control statements like if/else, for loops, and while loops to structure code execution.
- Efficient MATLAB programming involves using built-in functions instead of custom functions, preallocating arrays, and avoiding nested loops where possible through matrix operations.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
The document discusses arrays and array data structures. It defines an array as a set of index-value pairs where each index maps to a single value. It then describes the common array abstract data type (ADT) with methods like create, retrieve, and store for manipulating arrays. The document also discusses sparse matrix data structures and provides an ADT for sparse matrices with methods like create, transpose, add, and multiply.
1. The document provides examples of various functions in R including string functions, mathematical functions, statistical probability functions and other statistical functions. Examples are given for functions like substr, grep, sub, paste etc. to manipulate strings and functions like mean, sd, median etc. for statistical calculations.
2. Examples are shown for commonly used probability distribution functions like dnorm, pnorm, qnorm, rnorm etc. Other examples include functions for binomial, Poisson and uniform distributions.
3. The document also lists various other useful statistical functions like range, sum, diff, min, max etc. with examples. Examples are provided to illustrate the use of these functions through loops and to create a matrix.
This document provides an overview of basic MATLAB concepts including:
1. Creating variables and performing basic arithmetic operations
2. Generating and manipulating matrices using built-in functions
3. Plotting graphs of simple functions like sine and cosine waves
4. Solving linear equations and finding the inverse and determinant of matrices
It includes sample exercises demonstrating these MATLAB skills.
1. The document discusses matrices and various matrix operations.
2. It defines what a matrix is and different types of matrices such as row matrix, column matrix, square matrix, diagonal matrix, triangular matrix, and null matrix.
3. It covers matrix addition and multiplication. Matrix addition involves adding corresponding elements of two matrices of the same size. Matrix multiplication is only defined if the number of columns of the first matrix equals the number of rows of the second matrix.
1) Matrices can be defined as row vectors, column vectors, or 2D matrices in MATLAB. Common operations include addition, subtraction, multiplication, and exponentiation.
2) Predefined functions like ones, zeros, eye, and rand can be used to create matrices. Other functions like sum, diag, transpose, inv, and det perform operations on matrices.
3) Matrices can be concatenated horizontally using [A B] or vertically using [A;B]. Elements can be indexed and extracted from matrices using normal, linear, or logical indexing.
This document provides an overview of MATLAB, including its common uses in engineering fields like rocket design, its basic commands and functions for mathematics, matrices, polynomials, and more. Key features of MATLAB covered include its command window, editor, predefined math functions, matrix commands using colons, reading and writing files, and basic programming statements.
This document provides an overview of plotting functions in MATLAB. It discusses how to generate basic and 3D plots, customize plots using options like color, style and labels, and control the plot appearance using functions such as axis, title, legend. Examples are given to illustrate plotting a simple function, holding multiple plots, using subplots, and generating surface plots. The document also covers plotting in 3D using functions like surf, plot3 and manipulating axes properties.
This document provides contact information for math assignment help, including a phone number and email address. It then presents solutions to several problems from a linear algebra textbook. The problems cover topics like writing a quadratic form as a sum of squares, finding the closest line and plane of best fit to a set of points, orthonormal vectors, and determinants. Solutions are provided in mathematical notation and include working steps.
The document defines matrices and their properties, including symmetric, skew-symmetric, and determinant. It provides examples of solving systems of equations using matrices and their inverses. It also discusses properties of determinants, including properties related to symmetric and skew-symmetric matrices. Inverse trigonometric functions are defined, including their domains, ranges, and relationships between inverse functions using addition and subtraction formulas. Sample problems are provided to solve systems of equations and evaluate determinants.
This document contains a 45 item multiple choice test on additional mathematics. It provides instructions for taking the test, including that it has 45 items to be completed in 1 hour and 30 minutes. It also lists some formulae provided on page 2. Each item has 4 answer choices labeled A, B, C, or D. Students are to record their answers on an answer sheet by shading the corresponding space for the choice they believe is best. A sample item is worked through as an example. Calculators may be used.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Design and optimization of ion propulsion dronebjmsejournal
Electric propulsion technology is widely used in many kinds of vehicles in recent years, and aircrafts are no exception. Technically, UAVs are electrically propelled but tend to produce a significant amount of noise and vibrations. Ion propulsion technology for drones is a potential solution to this problem. Ion propulsion technology is proven to be feasible in the earth’s atmosphere. The study presented in this article shows the design of EHD thrusters and power supply for ion propulsion drones along with performance optimization of high-voltage power supply for endurance in earth’s atmosphere.
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
2. inf infinity
pi Ratio of circle
exp ( degree ) Exponential
sin (radian) cos (radian) tan (radian)
sind (degree) cosd(degree) tand (degree)
X = 3 + 4i
real ( X ) = 3
imag ( X ) = 4
abd ( X ) = 5
angle ( X ) = 0.9273 Angle in radian
conj ( X ) = 3.0000 - 4.0000i
3. asin (Value) Inverse sin
acos (Value) Inverse cos
atan (Value) Inverse tan
sec cosec cot sinh cosh tanh sech cosech coth
Can add ( d ) to use in degree or add ( a ) in first to get inverse
sqrt ( Value ) Root
log ( Value ) Ln
log10 ( Value )
factorial ( Value )
round ( Value ) Closest number for value
4. Format long increase accuracy of number
Format short decrease accuracy of number
round ( Value ) Round nearest integer .5
fix ( Value ) Round toward zero
ceil ( Value ) Round toward infinity
floor ( Value ) Round toward minus infinity
rem ( X , Y ) Returns the remainder
sign ( X ) sign function. [ X>0 -> 1 , X<0 -> -1 , X=0 -> 0 ]
5. clc Clean command window
clear Delete all variable
clear all Delete all variable
clear A Delete variable A only
who Show all variables
& = and ( x , y ) And
~ = not( x ) Not
| = or( x , y ) Or
xor ( x, y ) Xor
7. Vector = [ a(1) a(2) a(3) a(4) a(5) ] Define vector by elements
X = [ 12 8 2 34 0 ]
X = [ A : B : C ] Define vector by steps
A : first element B : steps of counter C : last element
X = [ 1 : 2 : 5 ]
X = 1 3 5
X = [ 1 : 5 ] Define with one step by default
X = 1 2 3 4 5
8. If you write X = [ 12 8 2 34 0 ] on command window without ; (semi Colom)
Matlab will print it .
X = [ 12 8 2 34 0 ]
X =
12 8 2 34 0
But if write X = [ 12 8 2 34 0 ] ; ( with semi Colom ) the matlab will not print
it.
X = [ 12 8 2 34 0 ] ;
9. Print vector
X = [ 0 1 2 3 4 ]
answer = X ( 1 ) print element a( 1 ) = 0
answer = X ( 1 : 4 ) print from elements from 0 to 3
answer = X ( 1 : end ) print from elements from 0 to 4
answer = X ( 1 : end - 1 ) print from elements from 0 to 3
11. X = [ 1 2 3 ] Y = [ 4 5 6 ]
prod ( X ) Product all elements of vector
Answer = prod ( X ) = 1 * 2 * 3 * 4 = 24
dot ( X , Y ) Dot product of two vectors
Answer = 1*4 + 2*5 + 3*6 = 32
cross ( X , Y ) Cross product of two vectors
Answer = -3 6 -3
Sum (X) To sum all elements in matrix
Answer = 6
12. linspace ( A , B , C ) generates C points between A and B
A : first element B : last element C : number of elements
X = linspace ( 0 , 1 , 5 )
= 0 0.2500 0.5000 0.7500 1.0000
X = linspace ( 0 , 1 , 6 )
= 0 0.2000 0.4000 0.6000 0.8000 1.0000
13. Define matrix
X = [ A B C ; D E F ] or X = [ A , B , C ; D , E , F ]
X = A B C Semi Colom to make new row
D E F
X = [ 1 : 0.5 : 2 ; 2 : -0.5 : 1 ] Different way to define
X = 1 1.5 2
2 1.5 1
14. Print matrix
X = [ 1 2 5 ; 0 1 7 ; 2 3 4 ]
X (1 , 3) = X ( A ( 1 ) , B ( 3 ) )
= 5
X (end - 1 , end - 2 ) = X ( A ( 2 ) , B ( 1 ) )
= 0
X (end , end) = X ( A ( 3 ) , B ( 3 ) )
= 4
16. Delete Elements
Define by index number for row or column then equal with []
X = [ 1 2 5 8 ; 0 1 7 2 ; 6 2 3 4 ]
X = X (1 , : ) =[] Delete first row
= 0 1 7 2
6 2 3 4
X ( : , [ 1 3 ] ) = [] Delete first and third column
= 2 8
1 2
2 4
17. Add Elements
Define by index number for row or column then equal with elements
X = [ 1 2 5 ; 0 1 7 ; 6 2 3 ]
X = X ( 4 , : ) = [ 0 0 0 ] Adding row in last
= 1 2 5
0 1 7
6 2 3
0 0 0
18. Operations on matrix
X = [ 1 2 : 3 4 ] Addition on matrix
Answer = X + 5
Answer = 6 7
8 9
rand ( A , B ) Make matrix with random values
A : Number of rows B : Number of columns
X = prod ( 2 , 3 )
0.8147 0.1270 0.6324
0.9058 0.9134 0.0975
19. E–notation
E – 1 = 0.1
E – 2 = 0.01
9E - 1 = .9
4E - 2 = .04
X = [ 5E-1 7E-2 9e-4]
= 0.5000 0.0700 0.0009
It can be e or E
20. Complex Numbers
•Both i and j are allowed
•Don’t write I nor J
•Write 3i and don’t write i3
•You can write 3*i or i*3
X = [ 1 + 3i ; 5 - 1i ; 4 + 3j ]
1.0000 + 3.0000i
5.0000 - 1.0000i
4.0000 + 3.0000i
24. magic ( N ) Make square matrix with random values
X= magic ( 2 ) N : number of raw or column
= 1 3
4 2
reshape ( A , B , C ) Reshape the size of matrix
A : Name of matrix B : Row of new matrix C : Column of new matrix
answer= reshape ( X , 2 ,3 ) // X = [ 1 2 ; 3 4 ; 5 6 ]
= 1 5 4
3 2 6
25. X = [ 1 2 3 ; 4 5 6 ]
max ( X ) Maximum element in matrix
= 6
min ( X ) Minimum element in matrix
= 1
size ( X ) Size of matrix
= 2 3 2 is raw , 3 is column
length ( X ) Number of columns in matrix
= 3
26. X = [ 1 2 3 ; 4 5 6 ]
fliplr ( X ) Replace columns from left to right
= 3 2 1
6 5 4
flipud ( X ) Replace rows from up to down
= 4 5 6
1 2 3
27. X = [ 1 2 3 ; 4 5 6 ]
transpose ( X ) = X ' Make rows to columns
= 1 4
2 5
3 6
rot90 ( X ) Rotate matrix 90 degree anti-clockwise
= 3 6
2 5
1 4
28. X = [ 1 2 ; 4 5 ] Y = [ 6 7 ; 8 9 ]
Product matrix element by element (square element)
Answer = X . * Y
= 6 1 4
3 2 4 5
Division in matrix element by element
Answer = X . / Y
= 0.1667 0.2857
0.5000 0.5556
29. X = [ 1 2 ; 4 5 ]
Product and matrix ( cross product )
X*X = X^2
= 7 1 0
1 5 2 2
Product matrix by number
Answer = X * 2
= 2 4
6 8
30. X = [ 1 2 ; 4 5 ]
Division in matrix by number (using / )
Answer = X / 2
= 0.5000 1.0000
1.5000 2.0000
Division in matrix to solve equations (using )
By invers matrix ( power -1 )
x + y = 2
x - y = 0
31. A ^ - 1 * B = inv( A ) * B = A B is up of enter key
B * A ^ - 1 = B * inv( A ) = B A
A X B
A = [ 1 1 ; 1 -1 ] B = [ 2 ; 0 ]
X = A B = inv (A) * B
answer = 1 x=1 y=1
1
32. X = [ 1 2 3 ; 4 5 6 ]
Power in matrix power elements
Answer = X.^2
= 1 4 9
16 25 36
Power to product in matrix ( cross product )
Answer = X^2 = X*X Must dimension allow
= Error
33. A = [ 1 2 ; 3 4 ] B = [ 1 -1 ; 2 -2 ]
Power in matrix by matrix
Answer = A.^B
= 1.0000 0.5000
9.0000 0.0625
The determinant in matrix ( | المحددة | )
det (A) = -2
det (B) = 0
34. A = [ 1 2 ; 3 4 ] Matrix
B = [ 10 -1 2 -2 ] Vector
sum ( Matrix ) Sum elements in each column
sum ( A ) = 4 6
But in vector the sum for row
sum ( B ) = 9
35. A = [ 1 2 5 ; 0 1 7 ; 2 3 4 ]
rank ( Matrix ) provides an estimate of the number of linearly independent
rows or columns of matrix.
rank ( A ) = 3
trace ( Matrix ) Sum of the diagonal elements
trace ( A ) = 6
36. pascal ( N ) Make random square matrix like magic (N)
N : number of row or column
pascal (3) = 1 1 1
1 2 3
1 3 6
diag ( A ) It is main diagonal elements of matrix
A = [ 1 2 5 ; 0 1 7 ; 6 2 3 ]
diag ( A ) = 1
1
3
Remember trace ( A ) get the sum of diag ( A ) = 5
38. X = [ 0 pi/4 pi/2 pi ] Y = sin ( X )
plot ( A , B ) Drawing F(A) horizontal axis and F (B) Vertical axis
plot ( X , Y )
The problem is low
number of data points
no figure .
X vector is 4 points only.
So on Y function.
39. The solution by increase input data points in X vector by :
X = [ 0 : 0.01 : pi ] ; Y = sin ( X ) ;
plot ( X , Y )
In X vector increase point .Start form 1
to pi using steps 0.01 that data points
( increase accuracy ).
You can put ; after X and Y to don't
print the vector again
40. X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
plot ( X , Y )
Print sin function start from 0 degree
To 360 degree using 1 degree step.
plot ( X , Y ) = plot ( X , Y ) ;
If you put ; after plot ( X ,Y ) or
don't put the same.
41. X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
To change color of figure
plot ( X , Y , 'r')
Black ‘k'
Yellow ‘y'
Magenta ‘m'
Cyan ‘c'
Red 'r'
Green ‘g'
Blue ‘b'
42. X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
To draw grid on figure:
grid on
To turn of the grid:
grid off
Line marking:
Change line to be . + * o >
Put after color in the ‘ '
plot ( X , Y , 'r+')
43. + plus sign
o circle
* asterisk
. Point
x cross
s square
d diamond
^ upward pointing triangle
v downward pointing triangle
> right pointing triangle
< left pointing triangle
p five-pointed star (pentagram)
h six-pointed star (hexagram)
44. Line Styles:
- solid line (default)
-- dashed line
: dotted line
-. dash-dot line
plot ( X , Y , '- - ' )
You can use line style or line mark
without color and can use them together
plot ( X , Y , '* - -' )
45. Multiple plot:
To plot multiple plots on the same
figure use the command:
hold on
X = [ 0 : . 01 : 10 ] ;
Y = X . ^ 2;
A = 3 * X ;
plot ( X , Y , 'r - -' )
hold on
plot ( X , A , 'c ' )
46. Multiple plot:
To plot multiple plots on the same
figure use the command:
plot (X,Y,A ,B)
grid on
X = [ 0 : . 01 : 10 ] ;
Y = X . ^ 2 ;
A = 3 * X ;
plot ( X , Y, 'b', X ,A , 'k ')
47. Adding Titles and Axes Labels :
title xlabel ylabel
grid on
A = [ 0 : . 01 : 10 ] ;
B = A . ^ 3;
plot ( A , B, 'c ')
title (' Two functions ')
xlabel (' A axis ' )
ylabel (' B axis ' )
Don't forget ' ' around text
48. Legend:
Legend is used when dealing
with multiple plots.
A = [ 0 : . 01 : 10 ] ;
B = A . ^ 2;
C = sqrt ( A ) ;
plot(A ,B, 'r ',A , C , 'g --') ;
legend ( 'square', 'root') ;
Square : first plot < A , B >
Root : second plot < A , C >
legend
49. subplot ( A , B , C ):
Divide the MATLAB plot window into sub-plot windows
A : number of rows.
B : number of columns.
C : wanted plot to drawing.
X = [ 0:0.01: 2*pi];
Y = sin (X );
s u bplot(1 , 2,1)
p l ot( X ,Y, 'r')
Z = X .^ 3;
s u bplot(1 , 2,2)
p l ot( X ,Z, 'k')
50. linewidth:
Change line style or line mark line size by :
plot(x,y,'linewidth',2)
plot(X,Y,'g-','linewidth',3)
fontsize:
Change title , xlabel or ylabel font size by :
title ( ' Sample Plot ' ,'fontsize', 14 ) ;
xlabel ( ' X values ' , ' fontsize ' , 14 ) ;
ylabel ( ' Y values ' , ' fontsize ' , 14 ) ;
52. Function plot:
fplot ( @X , [ A Z ] , 'r--+')
X : standard function to drawing
( sin exp sind acos sqrt log )
A : start substitution
Z : end substitution
fplot ( @sin , [ 0 2*pi ] , 'm--')
53. Function plot:
You can use:
fplot ( 'X' , [ A Z ] , 'r--+')
But will get warning
fplot ( 'sin' , [ 0 2*pi ] , 'm--')
54. Function plot:
Draw without period
fplot ( @X ,'r--+')
fplot ( 'X' ,'r--+')
fplot ( @exp , 'm')
fplot ( 'exp' , 'm')
58. figure : This command make new figure to draw new plot.
X=[ 0 : 1 : 360 ];
Y = sind (X);
Z = cosd (X);
plot(X,Y)
grid on
figure
plot(X,Z)
grid on
Figure 1 Figure 2
67. To make m-file press N + ctrl or select New then script .
First rule in programming end every command with ;
X = input (' Text ') ; To receive value form user
X = input (' Text ' , 's') ; To receive text form user
X : The variable that the input will be saved in it.
Text : Told user what to enter.
X = input (' Enter the temperature ') ; Enter 2023
X = input (' Enter your name ' , 's') ; Enter Ahmed
68. Print text or print variable:
disp ( X ); Print the saved value in variable X
disp ( 'X' ); Print X letter
Area = 2 * pi * 10;
disp ( area ); Print 62.831853
disp ( 'area' ); Print area
You can not print variable and text together
69. Commands:
%
Any thing will be writhen after % called comment and will not read from matlab
% Matlab is big program
n Get new line (should put it every display command)
disp ( 'area n of circle' ); Print area
of circle
70. Area = 62.831853 length= 20
If you print integer number use %d else if float number use %f
fprintf ('the area of circle = %f - %d n' , Area, length);
the area of circle = 62.831853 , 20
fprintf ('% 12.3 f ' , Area);
12 Present on space in printing
.3 Present number of fractions after . In float numbers
fprintf ('the area of circle = %0.2f n' , Area);
the area of circle = 62.83
72. Price=input('Enter the price=n');
if Price == 2000
Discount = .5;
elseif Price >1000
Discount = .3;
else
Discount = .1;
end
Price = Price – Price * Discount;
price == 2000 used to check equal
73. for statement:
for variable = condition
Statement;
end
condition : initial value : increment : end value
Result = 1; Factorial command
for X = 1 : 5
Result = Result * X;
end
74. i =input('Enter number of rows=n');
j =input('Enter number of columns=n');
for A = 1 : i
for B = 1 : j
X( A , B )=input('Enter the value =n');
end
end
disp(X)
77. X=input(‘Enter the case number =n’);
switch X
case 1
disp (' one ');
case 2
disp (' two ');
otherwise
disp (' error ');
end
78. X=input('Enter the case letter =n','s');
switch X
case 'A'
disp (' a letter ');
case 'B'
disp (' B letter ');
otherwise
disp (‘ error ');
end
79. Break:
Use break to exit the loop ( for , while ).
for i = 1 : 360
X = sind(i);
if(X==1)
break;
end
end
fprintf (' X = %d n Angle = %d degree n', X , i );
80. To make function-file select New then function.
function [outputArg1,outputArg2] = untitled (inputArg1,inputArg2)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
outputArg1 = inputArg1;
outputArg2 = inputArg2;
end
First look when open function file
untitled title of function
outputArg1,outputArg2 Outputs
inputArg1,inputArg2 Inputs
81. function [Area_of_circle] = Area(Diameter)
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
format long
Area_of_circle = (Diameter^2)*.25 * pi;
end
Function called Area calculate area of circle by one input Diameter and one output
Area_of_circle
Area (10) Calling in command
ans = 78.539816339744831
82. function [Area , Distance] = Circle(Diameter)
% Area of circle Function calculate Area and Circumference
% Distance : Circumference of circle
Area = (Diameter ^ 2 )*.25*pi;
Distance = Diameter*pi;
end
Use next expression when have two or more outputs
[ Area Distance ] = Circle (10)
Area =
78.5398
Distance =
31.4159
83. Symbols in matlab:
syms X Y Z T Define symbols
A = X^2 – 2*X +1
B = X^2 - 16
C = X^3 + X^2 + 2*X +1
solve ( Equation == 0 ) Solving equations for all degrees
But must define symbols at first syms X
solve ( X - 1 == 0) >>> X = 1
solve (X^2 - 10*X + 16 == 0) >>> X= 2 8
84. Solving equations together:
Define symbols then put the unknown symbols in [ ] then equal it to
solve (equations in one side equal to zero )
Solve A = X - Y = 6 , B = X + Y = -2
syms X Y
[ X Y ] = solve ( X - Y - 6 , X + Y + 2 )
X = 2 Y = - 4
85. Differentiation:
Define symbols then diff ( Equation )
syms x
Y = x^3 + x^2 + 2*x +1
diff ( Y )
Answer = 3*x^2 + 2*x + 2
By default matlab differentiate for x ( small letter )
86. Differentiation for any symbol and more than one:
syms X
Y = X^3 + X^2 + 2*X +1
diff ( Y , X ) Differentiate for X symbol
Answer = 3*X^2 + 2*X + 2
diff ( Y , 2 ) or diff ( diff ( Y ) ) Differentiate twice
Answer = 6*X + 2
87. Substitution in Differentiation:
subs ( Answer , [ A B X ] , [ 1 2 3] )
syms X A B
Y = A*X^3 + B*X^2 + 2*X +1
Answer = diff ( Y , X )
Answer = 3*A*X^2 + 2*B*X + 2
subs ( Answer , [ A B X ] , [ 1 2 3] )
ans = 41
88. Simple in Differentiation:
simplify ( Answer ) Simple the answer of differentiation
syms X
Y = X^3 * exp ( - X^2) * sin ( X )
Answer = diff ( Y , X )
Answer = X^3*exp (-X^2)*cos(X) + 3*X^2*exp (-X^2)*sin(X) - 2*X^4*exp(-
X^2)*sin(X)
simplify ( Answer )
ans = X^2*exp(-X^2)*(3*sin(X) + X*cos (X) - 2*X^2*sin(X))
90. Integration:
Define symbols then int ( Equation )
syms x
Y = x^3 + x^2 + 2*x +1
int ( Y )
Answer = x^4/4 + x^3/3 + x^2 + x
By default matlab integrate for x ( small letter )
91. Integration for any variable :
int ( Equation , Integration for )
syms X Y
F = Y*X^3 + + Y^2+X^2 + 2*Y^3*X +1
int ( F , Y )
Answer = (X*Y^4)/2 + Y^3/3 + Y*(X^2 + 1) + (X^3*Y^2)/2
For integration more than one time:
int ( int ( F ) )
Answer = (X^5*Y)/20 + X^2*(Y^2/2 + 1/2) + X^4/12 + (X^3*Y^3)/3
92. Substitution in integration :
int ( Equation , Integration for , Star , End )
syms X
Y = 3*X^2 + 2*X + 1
int ( Y , X , 0 , 1 )
Answer = 3
You can use command subs ( ) :
subs ( Answer , [ X ] , [ 1 ] ) - subs ( Answer , [ X ] , [ 0 ] )
93. Integration for X then for Y and substitution:
syms X Y
F = Y*X^3 + Y^2 + X^2 + 2*Y^3*X +1
int ( int ( F , X , 0 , 1 ) , Y , 0 , 2 )
Answer = 59/6
Wil integrate F for X and substitution form 0 to 1 then integrate answer for Y
and substitution form 0 to 2
94. Limits:
Define symbols then limit ( Equation , limit by , limit to )
syms X
Y = sin ( X ) / X
limit ( Y , X , 0 )
Answer = 1
By default matlab do limits without define ( limit by ) if there are one symbol
in equation only ( Equation has X or Y not X and Y )
limit ( Y , 0 )
95. Partial fraction for numerical:
[ C , D , E ] = residue ( A , B )
A = [ - 4 8 ];
B = [ 1 6 8 ];
[ C D E ] = residue ( A , B )
C = - 12 8 D = - 4 - 2 E = []
You can change A,B,C,D and E with any symbols but the arrangement
required the first is numerator and the second is maqam.
[ r p k ] = residue ( b , a ) == [ C D E ] = residue ( A , B )
96. When define A and B must arrange power and if power missed equal zero
Y = (x^2+5)/(x^3+2*x)
A = [ 1 0 1 ] ;
B = [ 1 0 2 0 ] ;
[C D E] = residue ( A , B )
C = 0.2500 0.2500 0.5000
D = 0.0000 + 1.4142i 0.0000 - 1.4142i 0.0000 + 0.0000i
E = [ ]
97. The unification of the stations:
[ A , B ] = residue ( C , D , E )
Must C and D vertical matrix (one column))
C = [ - 12 ; 8 ];
D = [ - 4 ; - 2 ];
E = [];
[ A B ] = residue (C , D , E )
A = - 4 8 B = 1 6 8
98. Partial fraction for symbols:
syms X
A = - 4*X+8 ;
B = X^2+6*X+8 ;
diff ( int ( A / B ) )
Answer = 8/(X + 2) - 12/(X + 4)
More better diff ( int ( A / B , X ) , X )