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Chapter 70
Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015

70.1 Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
70.2 Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
70.3 Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
70.4 Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
70.5 Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
70.6 Chapter 3. Systems of two first order equations. Section 3.2 (Two first order linear differential equations). Problems at page 142
70.7 Chapter 3. Systems of two first order equations. Section 3.3 (Homogeneous linear systems with constant coefficients). Problems at page 165
70.8 Chapter 3. Systems of two first order equations. Section 3.4 (Complex Eigenvalues). Problems at page 177
70.9 Chapter 3. Systems of two first order equations. Section 3.5 (Repeated Eigenvalues). Problems at page 188
70.10 Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
70.11 Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
70.12 Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
70.13 Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
70.14 Chapter 4. Second order linear equations. Section 4.4 (Mechanical and electrical vibration). Problems at page 250
70.15 Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
70.16 Chapter 4. Second order linear equations. Section 4.6 (Forced vibrations, Frequency response, and Resonance). Problems at page 272
70.17 Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
70.18 Chapter 5. The Laplace transform. Section 5.2 (Properties of the Laplace transform). Problems at page 309
70.19 Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
70.20 Chapter 5. The Laplace transform. Section 5.6 (Differential equations with Discontinuous Forcing Functions). Problems at page 342
70.21 Chapter 5. The Laplace transform. Section 5.7 (Impulse Functions). Problems at page 350
70.22 Chapter 5. The Laplace transform. Section 5.8 (Convolution Integrals and Their Applications). Problems at page 359
70.23 Chapter 6. Systems of First Order Linear Equations. Section 6.1 (Definitions and examples). Problems at page 388
70.24 Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
70.25 Chapter 6. Systems of First Order Linear Equations. Section 6.3 (Homogeneous Linear Systems with Constant Coefficients). Problems at page 408
70.26 Chapter 6. Systems of First Order Linear Equations. Section 6.4 (Nondefective Matrices with Complex Eigenvalues). Problems at page 419
70.27 Chapter 6. Systems of First Order Linear Equations. Section 6.5 (Fundamental Matrices and the Exponential of a Matrix). Problems at page 430
70.28 Chapter 6. Systems of First Order Linear Equations. Section 6.6 (Nonhomogeneous Linear Systems). Problems at page 436
70.29 Chapter 6. Systems of First Order Linear Equations. Section 6.7 (Defective Matrices). Problems at page 444
70.30 Chapter 7. Nonlinear Differential Equations and Stability. Section 7.1 (Autonomous Systems and Stability). Problems at page 464

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