Preface .................................................... vii
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 .............................. 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
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