**PART A Ordinary Differential Equations (ODEs)**

1.2 Geometric Meaning of *y*′ = *f*(*x*, *y*). Direction Fields, Euler's Method

1.4 Exact ODEs. Integrating Factors

1.5 Linear ODEs. Bernoulli Equation. Population Dynamics

1.6 Orthogonal Trajectories. *Optional*

1.7 Existence and Uniqueness of Solutions for Initial Value Problems

Chapter 1 Review Questions and Problems

CHAPTER 2 Second-Order Linear ODEs

2.1 Homogeneous Linear ODEs of Second Order

2.2 Homogeneous Linear ODEs with Constant Coefficients

2.3 Differential Operators. *Optional*

2.4 Modeling of Free Oscillations of a Mass–Spring System

2.6 Existence and Uniqueness of Solutions. Wronskian

2.8 Modeling: Forced Oscillations. Resonance

2.9 Modeling: Electric Circuits

2.10 Solution by Variation of Parameters

Chapter 2 Review Questions and Problems

CHAPTER 3 Higher Order Linear ODEs

3.2 Homogeneous Linear ODEs with Constant Coefficients

3.3 Nonhomogeneous Linear ODEs

Chapter 3 Review Questions and Problems

CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods

4.0 For Reference: Basics of Matrices and Vectors

4.1 Systems of ODEs as Models in Engineering Applications

4.2 Basic Theory of Systems of ODEs. Wronskian

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