2. Chapter 14
Partial Derivatives

3. Domains and Ranges Example Chapter 14
14.1 Functions of Several Variables
Domains and Ranges
Example

4. 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.

5. Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables

6. Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables

7. Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Functions of Two Variables
Example

8. Graphs, Level Curves, and Contours of Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables

9. Graphs, Level Curves, and Contours of Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables
Example

10. Graphs, Level Curves, and Contours of Functions of Two Variables
Chapter 14
14.1 Functions of Several Variables
Graphs, Level Curves, and Contours of Functions of Two Variables

11. Functions of Three Variables
Chapter 14
14.1 Functions of Several Variables
Functions of Three Variables
Example

12. Functions of Three Variables
Chapter 14
14.1 Functions of Several Variables
Functions of Three Variables

13. Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits

14. Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits

15. Limits Example Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
Example

16. Limits Example Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Limits
Example

17. Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity

18. Continuity Example Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
Example

19. Continuity Example Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity
Example

20. Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Continuity

21. Homework 4 Exercise 13.5, No. 12. Exercise 13.5, No. 24.
Chapter 14
14.2 Limits and Continuity in Higher Dimensions
Homework 4
Exercise 13.5, No. 12.
Exercise 13.5, No. 24.
Exercise 14.1, No. 10.
Exercise 14.1, No. 24.
Exercise 14.2, No. 15.
Exercise 14.2, No. 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