Partial Derivatives of a Function of Two Variables
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Dr.-Ing. Erwin SitompulPresident University
Lecture 5
Multivariable Calculus
President University Erwin Sitompul MVC 5/1
http://zitompul.wordpress.com
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President University Erwin Sitompul MVC 5/2
Partial Derivatives of a Function of Two VariablesChapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/3
Partial Derivatives of a Function of Two VariablesChapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/4
Partial Derivatives of a Function of Two VariablesChapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/5
Partial Derivatives of a Function of Two VariablesChapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/6
Calculations Example
Chapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/7
Calculations Example
Chapter 14 14.3 Partial Derivatives
Example
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President University Erwin Sitompul MVC 5/8
Calculations Example
Chapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/9
Calculations Example
Chapter 14 14.3 Partial Derivatives
As a single-variable function,
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President University Erwin Sitompul MVC 5/10
Functions of More Than Two Variables Example
Chapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/11
Second-Order Partial Derivatives Example
Chapter 14 14.3 Partial Derivatives
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President University Erwin Sitompul MVC 5/12
The Mixed Derivative TheoremChapter 14 14.3 Partial Derivatives
Example
How?
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President University Erwin Sitompul MVC 5/13
Functions of Two and Three VariablesChapter 14 14.4 The Chain Rule
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President University Erwin Sitompul MVC 5/14
Functions of Two and Three VariablesChapter 14 14.4 The Chain Rule
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President University Erwin Sitompul MVC 5/15
Functions of Two and Three VariablesChapter 14 14.4 The Chain Rule
Example
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President University Erwin Sitompul MVC 5/16
Functions of Two and Three VariablesChapter 14 14.4 The Chain Rule
Example
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President University Erwin Sitompul MVC 5/17
Functions Defined on SurfacesChapter 14 14.4 The Chain Rule
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President University Erwin Sitompul MVC 5/18
Functions Defined on SurfacesChapter 14 14.4 The Chain Rule
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President University Erwin Sitompul MVC 5/19
Functions Defined on SurfacesChapter 14 14.4 The Chain Rule
Example
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President University Erwin Sitompul MVC 5/20
Functions Defined on SurfacesChapter 14 14.4 The Chain Rule
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President University Erwin Sitompul MVC 5/21
Functions Defined on SurfacesChapter 14 14.4 The Chain Rule
Example
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President University Erwin Sitompul MVC 5/22
Homework 5 Exercise 14.3, No. 14. Exercise 14.3, No. 43. Exercise 14.4, No. 5. Exercise 14.4, No. 12. Exercise 14.4, No. 40.
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: One week after midterm exam, at 17.15.
Chapter 14 14.4 The Chain Rule