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Second-Order Linear ODEs ; Applied Mathematics Three; chapter 2 ;February 3, 2023
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CHAPTER 2 Second-Order Linear ODEs 46
2.1 Homogeneous Linear ODEs of Second Order 46
2.2 Homogeneous Linear ODEs with Constant Coefficients 53
2.3 Differential Operators. Optional 60
2.4 Modeling of Free Oscillations of a Mass–Spring System 62
2.5 Euler–Cauchy Equations 71
2.6 Existence and Uniqueness of Solutions. Wronskian 74
2.7 Nonhomogeneous ODEs 79
2.8 Modeling: Forced Oscillations. Resonance 85
2.9 Modeling: Electric Circuits 93
2.10 Solution by Variation of Parameters 99
Chapter 2 Review Questions and Problems 102
Summary of Chapter 2 1
2.1 Homogeneous Linear ODEs of Second Order 46
2.2 Homogeneous Linear ODEs with Constant Coefficients 53
2.3 Differential Operators. Optional 60
2.4 Modeling of Free Oscillations of a Mass–Spring System 62
2.5 Euler–Cauchy Equations 71
2.6 Existence and Uniqueness of Solutions. Wronskian 74
2.7 Nonhomogeneous ODEs 79
2.8 Modeling: Forced Oscillations. Resonance 85
2.9 Modeling: Electric Circuits 93
2.10 Solution by Variation of Parameters 99
Chapter 2 Review Questions and Problems 102
Summary of Chapter 2 1
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