Multivariate Calculus Mathematics UIN Maliki Malang

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MULTIVARIATE
CALCULUS
Abdul Aziz, M.Si
Mathematics Department Science and Technology Faculty
The State of Islamic University Maulana Malik Ibrahim
Malang

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Lecture Schedules
 Class A :
Monday / 06.30 - 09.00 / B 208
 Class B :
Friday / 09.00 - 11.30 / B 207
 Class C :
Thursday / 09.00 - 11.30 / B 207
 Class D :
Monday / 09.00 - 11.30 / B 208

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MAIN LITERATURE

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Three-dimensional surfaces have high points and low
points that are analogous to the peaks and valleys
of a mountain range. In this chapter we will use
derivatives to locate these points and to study other
features of such surfaces.

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PARTIAL DERIVATIVES
In this chapter we will extend many of the basic concepts
of calculus to functions of two or more variables,
commonly called functions of several variables. We will
begin by discussing limits and continuity for functions
of two and three variables, then we will define
derivatives of such functions, and then we will use
these derivatives to study tangent planes, rates of
change, slopes of surfaces, and maximization and
minimization problems. Although many of the basic
ideas that we developed for functions of one variable
will carry over in a natural way, functions of several
variables are intrinsically more complicated than
functions of one variable, so we will need to develop
new tools and new ideas to deal with such functions.

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FUNCTION OF
SEVERAL VARIABLES
A function f of two variables, x and y, is a rule that
assigns a unique real number f(x, y) to each point (x, y)
in some set D in the xy-plane.
A function f of three variables, x, y, and z, is a rule that
assigns a unique real number f(x, y, z) to each point
(x,y,z) in some set D in three dimensional space.

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LEVEL CURVES

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EXAMPLE

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QUIZES
1.Sketch the contour plot of f(x, y) = 4x2+ y2 using level
curves of height for k = 0, 1, 2, 3, 4, 5.
2.Sketch the contour plot of f(x, y) = 2− x − y using level
curves of height k =−6, −4, −2, 0, 2, 4, 6.

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EXERCISES

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PARTIAL DERIVATIVES OF
FUNCTIONS OF TWO VARIABLES

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EXAMPLE

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PARTIAL DERIVATIVES VIEWEDAS
RATES OF CHANGE AND SLOPES

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IMPLICIT
PARTIAL DIFFERENTIATION

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QUIZES

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EXERCISES

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