Differential equations : C. Henry Edwards, David E. Penney ; with assistance of David Calvis.
Computing and modeling /
- 4th edition
- New Jersey : Pearson Prentice Hall, c2008.
- xii, 575 p. : ill. (some col.) ; 27 cm.
CONTENT
Chapter 1 First Order differential equations 1.1 Differential equations and mathematical models 1.2 Integrals as general and particular solutions 1.3 Slope fields and solution curves 1.4 Separable equations and applications 1.5 Linear first-order equations etc.
Chapter 2 Mathematical models and numerical methods 2.1 Population models 2.2 Equilibrium solutions and stability 2.3 Acceleration velocity 2.4 Numerical approximation: Euler's method 2.5 A closer look at the Euler method etc.
Chapter 3 Linear equations of higher order 3.1 Introduction: Second order linear equations 3.2 General solutions of linear equations 3.3 Homogeneous equations with constant coefficients 3.4 Mechanical vibrations 3.5 Nonhomogeneous equations and undetermined coefficient etc.
Chapter 4 Introduction to systems of differential equations 4.1 First-order systems and applications 4.2 The method of elimination 4.3 Numerical methods for systems
Chapter 5 Linear systems of differential equations 5.1 Matrices and linear systems 5.2 The Eigenvalue method for homogeneous systems 5.3 Second order systems and mechanical applications 5.4 Multiple Eigenvalue solutions 5.5 Matrix exponentials and linear systems etc.
Chapter 6 Nonlinear systems and phenomena 6.1 Stability and the phase plane 6.2 Linear and almost linear systems 6.3 Ecological models: Predators and competitors 6.4 Nonlinear mechanical systems 6.5 Chaos in dynamical systems
Chapter 7 Laplace transform methods 7.1 Laplace transforms and inverse transforms 7.2 Transformation of initial value problems 7.3 Translation and partial fractions 7.4 Derivatives, integrals, and products of transforms 7.5 Periodic and piecewise continuous input functions 7.6 Impulses and delta functions