, Solution Manual for
Mathematical Methods and Physical Insights
An Integrated Approach
(ISBN 9781107156418)
[Updated December 2022]
Alec J. Schramm
Occidental College
[Corrections? Please let me know: ]
©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception and
to the provisions of relevant collective licensing agreements, no reproduction of any part may
take place without the written permission of Cambridge University Press.
, Contents
2 Coordinating Coordinates page 1
3 Complex Numbers 8
4 Index Algebra 14
5 Brandishing Binomials 20
6 Series 27
7 Orbits in a Central Potential 46
8 Integration 50
9 Dirac Delta 67
10 Coda: Statistical Mechanics 73
11 Visualizing Vector Fields 75
12 Grad, Div & Curl 78
13 Interlude: Irrotational and Incompressible 85
14 Integrating Scalar and Vector Fields 87
15 The Theorems of Gauss and Stokes 98
16 Mostly Maxwell 109
17 Coda: Simply Connected Regions 113
18 Path Independence in the Complex Plane 115
19 Series, Singularities & Branches 122
2 ©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements, no reproduction of any
part may take place without the written permission of Cambridge University Press.
, 20 Interlude: Conformal Mapping 130
21 The Calculus of Residues 136
22 Coda: Analyticity & Causality 152
23 Prelude: Superposition 156
24 Vector Space 157
25 The Inner Product 159
26 Interlude: Rotations 170
27 The Eigenvalue Problem 182
28 Coda: Normal Modes 201
29 Cartesian Tensors 212
30 Beyond Cartesian 221
31 Prelude: 1 2 3 . . . Infinity 237
32 Eponymous Polynomials 239
33 Fourier Series 253
34 Convergence & Completeness 260
35 Interlude: Beyond the Straight & Narrow 264
36 Fourier Transforms 275
37 Coda: Of Time Intervals and Frequency Bands 294
38 First-Order ODEs 298
39 Second-Order ODEs 302
40 The Sturm-Liouville Problem 318
41 Partial Differential Equations 332
©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception 3
and to the provisions of relevant collective licensing agreements, no reproduction of any
part may take place without the written permission of Cambridge University Press.
Mathematical Methods and Physical Insights
An Integrated Approach
(ISBN 9781107156418)
[Updated December 2022]
Alec J. Schramm
Occidental College
[Corrections? Please let me know: ]
©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception and
to the provisions of relevant collective licensing agreements, no reproduction of any part may
take place without the written permission of Cambridge University Press.
, Contents
2 Coordinating Coordinates page 1
3 Complex Numbers 8
4 Index Algebra 14
5 Brandishing Binomials 20
6 Series 27
7 Orbits in a Central Potential 46
8 Integration 50
9 Dirac Delta 67
10 Coda: Statistical Mechanics 73
11 Visualizing Vector Fields 75
12 Grad, Div & Curl 78
13 Interlude: Irrotational and Incompressible 85
14 Integrating Scalar and Vector Fields 87
15 The Theorems of Gauss and Stokes 98
16 Mostly Maxwell 109
17 Coda: Simply Connected Regions 113
18 Path Independence in the Complex Plane 115
19 Series, Singularities & Branches 122
2 ©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements, no reproduction of any
part may take place without the written permission of Cambridge University Press.
, 20 Interlude: Conformal Mapping 130
21 The Calculus of Residues 136
22 Coda: Analyticity & Causality 152
23 Prelude: Superposition 156
24 Vector Space 157
25 The Inner Product 159
26 Interlude: Rotations 170
27 The Eigenvalue Problem 182
28 Coda: Normal Modes 201
29 Cartesian Tensors 212
30 Beyond Cartesian 221
31 Prelude: 1 2 3 . . . Infinity 237
32 Eponymous Polynomials 239
33 Fourier Series 253
34 Convergence & Completeness 260
35 Interlude: Beyond the Straight & Narrow 264
36 Fourier Transforms 275
37 Coda: Of Time Intervals and Frequency Bands 294
38 First-Order ODEs 298
39 Second-Order ODEs 302
40 The Sturm-Liouville Problem 318
41 Partial Differential Equations 332
©Alec J. Schramm 2022. This publication is in copyright. Subject to statutory exception 3
and to the provisions of relevant collective licensing agreements, no reproduction of any
part may take place without the written permission of Cambridge University Press.
