Synopses & Reviews
This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner. This is illustrated by over 250 worked out examples. The problems are extremely high quality and are regarded as one of the text's many strengths. This book also allows the instructor to select the level of technology desired. Trench has simplified this by using the symbols C and L. C exercises call for computation and/or graphics, and L exercises are laboratory exercises that require extensive use of technology. Several sections include informal advice on the use of technology. The instructor who prefers not to emphasize technology can ignore these exercises.
Table of Contents
1. INTRODUCTION Some Applications Leading to Differential Equations / Basic Concepts / Direction Fields for First Order Equations 2. FIRST ORDER EQUATIONS Linear First Order Equations / Separable Equations / Existence and Uniqueness of Solutions of Nonlinear Equations / Transformation of Nonlinear Equations into Separable Equations / Exact Equations / Integrating Factors 3. NUMERICAL METHODS Eulers Method / The Improved Euler Method and Related Methods / The Runge-Kutta Method 4. APPLICATIONS OF FIRST ORDER EQUATIONS Growth and Decay / Cooling and Mixing / Elementary Mechanics / Autonomous Second Order Equations / Applications to Curves 5. LINEAR SECOND ORDER EQUATIONS Homogeneous Linear Equations / Constant Coefficient Homogeneous Equations / Nonhomogenous Linear Equations / The Method of Undetermined Coefficients I / The Method of Undetermined Coefficients II / Reduction of Order / Variation of Parameters 6. APPLICATIONS OF LINEAR SECOND ORDER EQUATIONS Spring Problems I / Spring Problems II / The RLC Circuit / Motion Under a Central Force 7. SERIES SOLUTIONS OF LINEAR SECOND ORDER EQUATIONS Review of Power Series / Series Solutions Near an Ordinary Point I / Series Solutions Near an Ordinary Point II / Regular Singular Points; Euler Equations / The Method of Frobenius I / The Method of Frobenius II / The Method of Frobenius III 8. LAPLACE TRANSFORMS Introduction to the Laplace Transform / The Inverse Laplace Transform / Solution of the Initial Value Problems / The Unit Step Function / Constant Coefficient Equations with Piecewise Continuous Forcing Functions / Convolution / Constant Coefficient Equations with Impulses 9. LINEAR HIGHER ORDER EQUATIONS Introduction to Linear Higher Order Equations / Higher Order Constant Coefficient Homogeneous Equations / Undetermined Coefficients for Higher Order Equations / Variation of Parameters for Higher Order Equations 10. LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS Introduction to Systems of Differential Equations / Linear Systems of Differential Equations / Basic Theory of Homogenous Linear Systems / Constant Coefficient Homogeneous Systems I / Constant Coefficient Homogenous Systems II / Constant Coefficient Homogenous Systems III / Variation of Parameters for Nonhomogenous Linear Systems / ANSWERS TO SELECTED EXERCISES / INDEX