SOLUTIONS MANUAL
, Contents
Preface page ix
1 Preliminary algebra 1
2 Preliminary calculus 17
3 Complex numbers and hyperbolic functions 39
4 Series and limits 55
5 Partial differentiation 71
6 Multiple integrals 90
7 Vector algebra 104
8 Matrices and vector spaces 119
9 Normal modes 145
10 Vector calculus 156
11 Line, surface and volume integrals 176
,12 Fourier series 193
13 Integral transforms 211
14 First-order ODEs 228
15 Higher-order ODEs 246
16 Series solutions of ODEs 269
17 Eigenfunction methods for ODEs 283
18 Special functions 296
19 Quantum operators 313
20 PDEs: general and particular solutions 319
21 PDEs: separation of variables and other methods 335
22 Calculus of variations 353
23 Integral equations 374
24 Complex variables 386
25 Applications of complex variables 400
26 Tensors 420
27 Numerical methods 440
28 Group theory 461
29 Representation theory 480
, 30 Probability 494
31 Statistics 519
vii
, Contents
Preface page ix
1 Preliminary algebra 1
2 Preliminary calculus 17
3 Complex numbers and hyperbolic functions 39
4 Series and limits 55
5 Partial differentiation 71
6 Multiple integrals 90
7 Vector algebra 104
8 Matrices and vector spaces 119
9 Normal modes 145
10 Vector calculus 156
11 Line, surface and volume integrals 176
,12 Fourier series 193
13 Integral transforms 211
14 First-order ODEs 228
15 Higher-order ODEs 246
16 Series solutions of ODEs 269
17 Eigenfunction methods for ODEs 283
18 Special functions 296
19 Quantum operators 313
20 PDEs: general and particular solutions 319
21 PDEs: separation of variables and other methods 335
22 Calculus of variations 353
23 Integral equations 374
24 Complex variables 386
25 Applications of complex variables 400
26 Tensors 420
27 Numerical methods 440
28 Group theory 461
29 Representation theory 480
, 30 Probability 494
31 Statistics 519
vii
