# Homework

Sec.

Section Title

Homework

Solutions

9.1

9.5

9.7

Vector Functions

The Directional Derivative

Divergence and Curl

3,11,20,25,28,41

3,6,9,13,21,30

8,14,23,30

9.5_sol

9.7_sol

9.8

9.9

Line Integrals

Line Integrals Independent of the Path

5,10,16,22,30

7,15,18,23,28

9.9_sol

9.12

9.13

Green’s Theorem

Surface Integrals

2,6,17,25

3,11,26,33

9.13 sol

9.14

9.16

Stokes’ Theorem

Divergence Theorem

3,6,14,17

2,4,11

9.14 sol

4.1

4.2

Definition of the Laplace transform

Inverse Transform, Transforms of Derivatives

3,5,17, 29,38,40(c)

5,13,15,19,35,36

4.1 sol

4.2 sol

4.3

4.4

4.5

Translation Theorems

Dirac Delta Function

8,13,20,24, 47,60,66

5,16,19(b),23,34, 45

4,8,12

4.3 sol

4.4 sol

4.5 sol

12.1

12.2

Orthogonal Functions

Fourier Series

6,12,16,18

4,6,16,20

12.1 sol

12.2 sol

12.3

12.4

Fourier Cosine and Sine Series

Complex Fourier Series

4,6,14,16,26,38

2,4,6,11

12.3 sol

12.4 sol

12.5

Sturm-Liouville Theorem

2,4,6,8,14

12.5 sol

12.6

# Bessel and Legendre Series

2,4,6,8,10,20

12.6 sol

13.1

13.3

Separable Partial Differential Equation

Heat Equation

2,10,14,18,20,24,28

2,4,6,8,10

13.1 sol

13.3 sol

13.4

13.5

Wave Equation

Laplace’s Equation

2,4,6,8,10,11

2,4,8,10,14

13.4 sol

13.5 sol

14.2

14.3

Problems in Polar and Cylindrical Coordinates

Problems in Spherical Coordinates

2,4,8,10

4,6,12

14.3 sol

15.2

# Applications of the Laplace Transform

6,8,10,14,28

15.2 sol

15.3

Fourier Integral Theorem,

4,8,12,18

15.3 sol

15.4

Fourier Transforms

6,10,12,18

15.4 sol