Chapter 14 Partial Derivatives. Chapter 14 Partial Derivatives.

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Presentation transcript:

Chapter 14 Partial Derivatives

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

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.

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

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

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

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

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

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

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

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

Chapter 14 14.2 Limits and Continuity in Higher Dimensions Limits

Chapter 14 14.2 Limits and Continuity in Higher Dimensions Limits

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

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

Chapter 14 14.2 Limits and Continuity in Higher Dimensions Continuity

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

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

Chapter 14 14.2 Limits and Continuity in Higher Dimensions Continuity

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 17.15.