Chapter 1 First-Order Odes 1.1 Basic Concepts. Modeling Problem Set p.8 1.2 Geometric Meaning of y'=f(x,y). Direction Fields, Euler's Method Problem Set p.11 1.3 Separable ODEs. Modeling Problem Set p.18 1.4 Exact ODEs.

Integrating Factors Problem Set p.26 1.5 Linear ODEs. Bernoulli Equation. Population Dynamics Problem Set p.34 1.6 Orthogonal Trajectories Problem Set p.38 1.7 Existence and Uniqueness of Solutions for Initial Value Problems Problem Set p.42 Review Questions and Problems p.43 Chapter 2 Second-Order Linear Odes 2.1 Homogeneous Linear ODEs of Second Order Problem Set p.53 2.2 Homogeneous Linear ODEs with Constant Coefficients Problem Set p.59 2.3 Differential Operators Problem Set p.61 2.4 Modeling of Free Oscillations of a Mass-Spring System Problem Set p.69 2.5 Euler-Cauchy Equations Problem Set p.73 2.6 Existence and Uniqueness of Solutions. Wronskian Problem Set p.79 2.7 Nonhomogeneous ODEs Problem Set p.84 2.8 Modeling: Forced Oscillations.

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Resonance Problem Set p.91 2.9 Modeling: Electric Circuits Problem Set p.98 2.10 Solution by Variation of Parameters Problem Set p.102 Review Questions and Problems p.102 Chapter 3 Higher Order Linear Odes 3.1 Homogeneous Linear ODEs Problem Set p.111 3.2 Homogeneous Linear ODEs with Constant Coefficients Problem Set p.116 3.3 Nonhomogeneous Linear ODEs Problem Set p.122 Review Questions and Problems p.122 Chapter 4 Systems Of Odes. Qualitative Methods 4.1 Systems of ODEs as Models in Engineering Applications Problem Set p.136 4.3 Constant-Coefficient Systems. Phase Plane Method Problem Set p.147 4.4 Criteria for Critical Points. Stability Problem Set p.151 4.5 Qualitative Methods for Nonlinear Systems Problem Set p.159 4.6 Nonhomogeneous Linear Systems of ODEs Problem Set p.163 Review Questions and Problems p.164 Chapter 5 Series Solutions Of Odes. Special Functions 5.1 Power Series Method Problem Set p.174 5.2 Legendre's Equation.

Legendre Polynomials Pn(x) Problem Set p.179 5.3 Extended Power Series Method: Frobenius Method Problem Set p.186 5.4 Bessel's Equation. Bessel Functions Jv(x) Problem Set p.195 5.5 Bessel Functions Yv(x). General Solution Problem Set p.200 Review Questions and Problems p.200 Chapter 6 Laplace Transforms 6.1 Laplace Transform. First Shifting Theorem (s-Shifting) Problem Set p.210 6.2 Transforms of Derivatives and Integrals.