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Chapter 14
Differential equations and their applications, 4th ed., M. Braun
14.1
Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
14.2
Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
14.3
Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
14.4
Chapter 1. First order differential equations. Section 1.10. Existence-uniqueness theorem. Excercises page 80
14.5
Chapter 1. First order differential equations. Section 1.17. What to do in practice. Excercises page 126
14.6
Chapter 2. Second order differential equations. Section 2.1. Algebraic properties of solutions. Excercises page 136
14.7
Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
14.8
Chapter 2. Second order differential equations. Section 2.2.1 Linear equations with constant coefficients (complex roots). Excercises page 144
14.9
Chapter 2. Second order differential equations. Section 2.2.2. Equal roots, reduction of order. Excercises page 149
14.10
Chapter 2. Second order differential equations. Section 2.4. The method of variation of parameters. Excercises page 156
14.11
Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
14.12
Chapter 2. Second order differential equations. Section 2.8. Series solutions. Excercises page 197
14.13
Chapter 2. Second order differential equations. Section 2.8.1, singular points, Euler equations. Excercises page 203
14.14
Chapter 2. Second order differential equations. Section 2.8.2, Regular singular points, the method of Frobenius. Excercises page 216
14.15
Chapter 2. Second order differential equations. Section 2.8.3, Equal roots and roots differing by an integer. Excercises page 223
14.16
Chapter 2. Second order differential equations. Section 2.9, The method of Laplace transform. Excercises page 232
14.17
Chapter 2. Second order differential equations. Section 2.10, Some useful properties of Laplace transform. Excercises page 238
14.18
Chapter 2. Second order differential equations. Section 2.11, Differential equations with discontinuous right-hand sides. Excercises page 243
14.19
Chapter 2. Second order differential equations. Section 2.12, Dirac delta function. Excercises page 250
14.20
Chapter 2. Second order differential equations. Section 2.14, The method of elimination for systems. Excercises page 258
14.21
Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
14.22
Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page 339
14.23
Section 3.9, Systems of differential equations. Complex roots. Page 344
14.24
Section 3.10, Systems of differential equations. Equal roots. Page 352
14.25
Section 3.12, Systems of differential equations. The nonhomogeneous equation. variation of parameters. Page 366
14.26
Chapter 3. Systems of differential equations. Section 3.13 (Solving systems by Laplace transform). Page 370
14.27
Chapter 4. Qualitative theory of differential equations. Section 4.1 (Introduction). Page 3770
14.28
Chapter 4. Qualitative theory of differential equations. Section 4.1 (Introduction). Page 377
14.29
Chapter 4. Qualitative theory of differential equations. Section 4.2 (Stability of linear systems). Page 383
14.30
Chapter 4. Qualitative theory of differential equations. Section 4.3 (Stability of equilibrium solutions). Page 393
14.31
Chapter 4. Qualitative theory of differential equations. Section 4.6 (Qualitative properties of orbits). Page 417
14.32
Chapter 4. Qualitative theory of differential equations. Section 4.7 (Phase portraits of linear systems). Page 427
14.33
Chapter 5. Separation of variables and Fourier series. Section 5.1 (Two point boundary-value problems). Page 480
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