1. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Elementary Examples a. Function of two variables, domain, range, p. 820 Function of two variables, domain, range, p. 820 b. Function of three variables, domain, range, p. 820 Function of three variables, domain, range, p. 820 A Brief Catalogue of …. a. Intercepts, traces, etc., p. 824 Intercepts, traces, etc., p. 824 b. Projections, p. 828, figure 14.2.10 Projections, p. 828, figure 14.2.10 Graphs; Level Curves and Level Surfaces a. Level curve, p. 831, figure 14.3.4 Level curve, p. 831, figure 14.3.4 b. Level surface, p. 835 Level surface, p. 835 Partial Derivatives a. Partial derivative with respect to x, y, p. 839 Partial derivative with respect to x, y, p. 839 b. Definition 14.4.1, p. 840 Definition 14.4.1, p. 840 c. Slope of the y 0 -section …, p. 841, figure 14.4.1 Slope of the y 0 -section …, p. 841, figure 14.4.1 d. Slope of the x 0 -section …, pp. 841, 842, figure 14.4.2 Slope of the x 0 -section …, pp. 841, 842, figure 14.4.2 e. Definition 14.4.2, p. 842 Definition 14.4.2, p. 842 f. Interpretations of partial derivatives, p. 843 Interpretations of partial derivatives, p. 843 Open and Closed Sets a. Definition 14.5.1, p. 847, 848, figure 14.5.1 Definition 14.5.1, p. 847, 848, figure 14.5.1 b. Definition 14.5.2, p. 848 Definition 14.5.2, p. 848 c. Definition 14.5.3, p. 848 Definition 14.5.3, p. 848 d. Definition 14.5.4, p. 848 Definition 14.5.4, p. 848 e. Definition 14.5.5, p. 849 Definition 14.5.5, p. 849 Limits and Continuity a. Limit of a function …, p. 851 Limit of a function …, p. 851 b. Continuity of composite functions, p. 854 Continuity of composite functions, p. 854 c. Equality of mixed partials, (14.6.5), p. 857 Equality of mixed partials, (14.6.5), p. 857 Chapter 14: Functions of Several Variables

2. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Elementary Examples Function of two variables, domain, range, p. 820

3. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Elementary Examples Function of three variables, domain, range, p. 820

4. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. A Brief Catalogue of… Intercepts, traces, etc., p. 824

5. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. A Brief Catalogue of… Projections, p. 828, figure 14.2.10

6. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Graphs; Level Curves and Level Surfaces Level curve, p. 831, figure 14.3.4

7. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Graphs; Level Curves and Level Surfaces Level surface, p. 835

8. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Partial derivative with respect to x, y, p. 839

9. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Definition 14.4.1, p. 840

10. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Slope of the y 0 -section…, p. 841, figure 14.4.1

11. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Slope of the x 0 -section…, p. 841, 842 figure 14.4.2

12. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Definition 14.4.2, p. 842

13. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Partial Derivatives Interpretations of partial derivatives, p. 843

14. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Open and Closed Sets Definition 14.5.1, p. 847, 848, figure 14.5.1

15. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Open and Closed Sets Definition 14.5.2, p. 848

16. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Open and Closed Sets Definition 14.5.3, p. 848

17. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Open and Closed Sets Definition 14.5.4, p. 848

18. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Open and Closed Sets Definition 14.5.5, p. 849

19. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Limits and Continuity Limit of a function…, p. 851

20. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Limits and Continuity Continuity of composite functions, p. 854

21. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Limits and Continuity Equality of mixed partials, (14.6.5), p. 857