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Dr.-Ing. Erwin Sitompul President University Lecture 5 Multivariable Calculus President UniversityErwin SitompulMVC 5/1

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Presentation on theme: "Dr.-Ing. Erwin Sitompul President University Lecture 5 Multivariable Calculus President UniversityErwin SitompulMVC 5/1"— Presentation transcript:

1 Dr.-Ing. Erwin Sitompul President University Lecture 5 Multivariable Calculus President UniversityErwin SitompulMVC 5/1 http://zitompul.wordpress.com

2 President UniversityErwin SitompulMVC 5/2 Partial Derivatives of a Function of Two Variables Chapter 1414.3 Partial Derivatives

3 President UniversityErwin SitompulMVC 5/3 Partial Derivatives of a Function of Two Variables Chapter 1414.3 Partial Derivatives

4 President UniversityErwin SitompulMVC 5/4 Partial Derivatives of a Function of Two Variables Chapter 1414.3 Partial Derivatives

5 President UniversityErwin SitompulMVC 5/5 Partial Derivatives of a Function of Two Variables Chapter 1414.3 Partial Derivatives

6 President UniversityErwin SitompulMVC 5/6 Calculations Example Chapter 1414.3 Partial Derivatives

7 President UniversityErwin SitompulMVC 5/7 Calculations Example Chapter 1414.3 Partial Derivatives Example

8 President UniversityErwin SitompulMVC 5/8 Calculations Example Chapter 1414.3 Partial Derivatives

9 President UniversityErwin SitompulMVC 5/9 Calculations Example Chapter 1414.3 Partial Derivatives As a single-variable function,

10 President UniversityErwin SitompulMVC 5/10 Functions of More Than Two Variables Example Chapter 1414.3 Partial Derivatives

11 President UniversityErwin SitompulMVC 5/11 Second-Order Partial Derivatives Example Chapter 1414.3 Partial Derivatives

12 President UniversityErwin SitompulMVC 5/12 The Mixed Derivative Theorem Chapter 1414.3 Partial Derivatives Example How?

13 President UniversityErwin SitompulMVC 5/13 Functions of Two and Three Variables Chapter 1414.4 The Chain Rule

14 President UniversityErwin SitompulMVC 5/14 Functions of Two and Three Variables Chapter 1414.4 The Chain Rule

15 President UniversityErwin SitompulMVC 5/15 Functions of Two and Three Variables Chapter 1414.4 The Chain Rule Example

16 President UniversityErwin SitompulMVC 5/16 Functions of Two and Three Variables Chapter 1414.4 The Chain Rule Example

17 President UniversityErwin SitompulMVC 5/17 Functions Defined on Surfaces Chapter 1414.4 The Chain Rule

18 President UniversityErwin SitompulMVC 5/18 Functions Defined on Surfaces Chapter 1414.4 The Chain Rule

19 President UniversityErwin SitompulMVC 5/19 Functions Defined on Surfaces Chapter 1414.4 The Chain Rule Example

20 President UniversityErwin SitompulMVC 5/20 Functions Defined on Surfaces Chapter 1414.4 The Chain Rule

21 President UniversityErwin SitompulMVC 5/21 Functions Defined on Surfaces Chapter 1414.4 The Chain Rule Example

22 President UniversityErwin SitompulMVC 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 1414.4 The Chain Rule

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