5.5 The Method of Undetermined Coefficients II 238
5.6 Reduction of Order 248
5.7 Variation of Parameters 255
Chapter 6 Applcations of Linear Second Order Equations 268
6.1 Spring Problems I 268
6.2 Spring Problems II 279
6.3 The RLC Circuit 291
6.4 Motion Under a Central Force 297
Chapter 7 Series Sol utions of Linear Second Order Equations
7.1 Review of Power Series 307
7.2 Series Solutions Near an Ordinary Point I 320
7.3 Series Solutions Near an Ordinary Point II 335
7.4 Regular Singular Points Euler Equations 343
7.5 The Method of Frobenius I 348
7.6 The Method of Frobenius II 365
7.7 The Method of Frobenius III 379
Chapter 8 Laplace Transforms
8.1 Introduction to the Laplace Transform 394
8.2 The Inverse Laplace Transform 406
8.3 So lution of Initial Va lue Problems 414
8.4 The Unit Step Function 421
8.5 Constant Coefficient Equations with Piecewise Continuous Forcing
Functions 431
8.6 Convolution 441
8.7 Constant Cofficient Equations with Impulses 453
8.8 A B ri ef Tabl e of Laplace Transforms
Chapter 9 Linear Higher Order Equations
9.1 Introduction to Linear Hig her Order Equations 466
9.2 Hi gher Order Constant Coefficient Homogeneous Equations 476
9.3 Undetermined Co efficients for Higher Order Equations 488
9.4 Variation of Parameters for Higher Order Equations 498
Chapter 10 Linear Systems of Differential E quations
10.1 Introduction to Systems of Dif ferentia l Equations 508
10.2 Linear Systems of Differential Equations 516
10.3 Basic Theory of Homogeneous Linear Systems 522
10.4 Constant Co efficient Homog eneous Systems I 530
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