Multivariable Calculus
Lecture 4
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
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Chapter 14
Partial Derivatives
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Chapter 14
14.1 Functions of Several Variables
Domains and Ranges
 Example
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Chapter 14
14.1 Functions of Several Variables
Domains and Ranges
 In defining a function of more than one variable, we follow the
usual practice of excluding inputs that lead to complex numbers
or division by zero.
 The domain of a function is assumed to be the largest set for
which the defining rule generates real numbers, unless the
domain is otherwise specified explicitly.
 The range of a function consists of the set of output values for
the dependent variable.
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Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables
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Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables
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Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables
 Example
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Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables
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Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables
 Example
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Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables
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Chapter 14
14.1 Functions of Several Variables
Functions of Three Variables
 Example
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Chapter 14
14.1 Functions of Several Variables
Functions of Three Variables
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
 Example
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
 Example
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
 Example
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
 Example
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
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Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Homework 4
 Exercise
 Exercise
 Exercise
 Exercise
 Exercise
 Exercise
13.5,
13.5,
14.1,
14.1,
14.2,
14.2,
No.
No.
No.
No.
No.
No.
12.
24.
10.
24.
15.
33.
 Homeworks must not be submitted, but there will be a 15-minute
short quiz in every lecture, asking 1-2 of the homework problems.
 Next short quiz: Next week, at 17.15.
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