A course in differential equations with boundary-value problems

著者

    • Wirkus, Stephen Allen
    • Swift, Randall J.
    • Szypowski, Ryan

書誌事項

A course in differential equations with boundary-value problems

Stephen A. Wirkus, Randall J. Swift, Ryan S. Szypowski

（Textbooks in mathematics）（A Chapman & Hall book）

CRC Press, Taylor & Francis Group, c2017

2nd ed

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注記

Previous title: A course in ordinary differential equations / Stephen A. Wirkus, Randall J. Swift (Boca Raton : CRC Press, 2015)

Includes bibliographical references (p. 755-757) and index

内容説明・目次

内容説明

A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author's successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student's field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB (R), Mathematica (R), and Maple (TM). The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB (R), Mathematica (R), and Maple (TM) are incorporated at the end of each chapter All three software packages have parallel code and exercises There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book

目次

Traditional First-Order Differential Equations Introduction to First-Order Equations Separable Differential Equations Linear Equations Some Physical Models Arising as Separable Equations Exact Equations Special Integrating Factors and Substitution Methods Bernoulli Equation Homogeneous Equations of the Form g(y=x) Geometrical and Numerical Methods for First-Order Equations Direction Fields|the Geometry of Differential Equations Existence and Uniqueness for First-Order Equations First-Order Autonomous Equations|Geometrical Insight Graphing Factored Polynomials Bifurcations of Equilibria Modeling in Population Biology Nondimensionalization Numerical Approximation: Euler and Runge-Kutta Methods An Introduction to Autonomous Second-Order Equations Elements of Higher-Order Linear Equations Introduction to Higher-Order Equations Operator Notation Linear Independence and the Wronskian Reduction of Order|the Case n = 2 Numerical Considerations for nth-Order Equations Essential Topics from Complex Variables Homogeneous Equations with Constant Coe cients Mechanical and Electrical Vibrations Techniques of Nonhomogeneous Higher-Order Linear Equations Nonhomogeneous Equations Method of Undetermined Coe cients via Superposition Method of Undetermined Coe cients via Annihilation Exponential Response and Complex Replacement Variation of Parameters Cauchy-Euler (Equidimensional) Equation Forced Vibrations Fundamentals of Systems of Differential Equations Useful Terminology Gaussian Elimination Vector Spaces and Subspaces The Nullspace and Column Space Eigenvalues and Eigenvectors A General Method, Part I: Solving Systems with Real and Distinct or Complex Eigenvalues A General Method, Part II: Solving Systems with Repeated Real Eigenvalues Matrix Exponentials Solving Linear Nonhomogeneous Systems of Equations Geometric Approaches and Applications of Systems of Differential Equations An Introduction to the Phase Plane Nonlinear Equations and Phase Plane Analysis Systems of More Than Two Equations Bifurcations Epidemiological Models Models in Ecology Laplace Transforms Introduction Fundamentals of the Laplace Transform The Inverse Laplace Transform Laplace Transform Solution of Linear Differential Equations Translated Functions, Delta Function, and Periodic Functions The s-Domain and Poles Solving Linear Systems Using Laplace Transforms The Convolution Series Methods Power Series Representations of Functions The Power Series Method Ordinary and Singular Points The Method of Frobenius Bessel Functions Boundary-Value Problems and Fourier Series Two-Point Boundary-Value Problems Orthogonal Functions and Fourier Series Even, Odd, and Discontinuous Functions Simple Eigenvalue-Eigenfunction Problems Sturm-Liouville Theory Generalized Fourier Series Partial Differential Equations Separable Linear Partial Differential Equations Heat Equation Wave Equation Laplace Equation Non-Homogeneous Boundary Conditions Non-Cartesian Coordinate Systems A An Introduction to MATLAB, Maple, and Mathematica MATLAB Some Helpful MATLAB Commands Programming with a script and a function in MATLAB Maple Some Helpful Maple Commands Programming in Maple Mathematica Some Helpful Mathematica Commands Programming in Mathematica B Selected Topics from Linear Algebra A Primer on Matrix Algebra Matrix Inverses, Cramer's Rule Calculating the Inverse of a Matrix Cramer's Rule Linear Transformations Coordinates and Change of Basis Similarity Transformations Computer Labs: MATLAB, Maple, Mathematica Answers to Odd Problems

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