CONTENTS
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
Get Advanced Engineering Mathematics, 10th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
