Synopses & Reviews
Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Synopsis
Written in a clear and accurate language that individuals can read and understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style and includes over 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths are its problems, which are consistently high quality.
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 11. FOURIER SERIES Homogeneous Boundary Value Problems for yn + Ay = 0 / Fourier Series I / Fourier Series II 12. PARTIAL DIFFERENTIAL EQUATIONS The Heat Equation / The Wave Equation / Laplaces Equation 13. BOUNDARY VALUE PROBLEMS Two Point Boundary Value Problems / Sturm-Liouville Problems / ANSWERS TO SELECTED EXERCISES / INDEX