A course in ordinary differential equations. (2015)

• Record Type: Book
• Further Information: Note: Stephen A. Wirkus, Randall J. Swift.
• Authors: Wirkus, Stephen Allen, 1971-; Swift, Randall J
• Contents: 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 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; Modeling in Population Biology; 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; Linear Independence and the Wronskian; Reduction of Order—the Case n = 2; Numerical Considerations for n th-Order Equations; Essential Topics from Complex Variables; Homogeneous Equations with Constant Coefficients; Mechanical and Electrical Vibrations Techniques of Nonhomogeneous Higher-Order Linear Equations; Nonhomogeneous Equations; Method of Undetermined Coefficients via Superposition; Method of Undetermined Coefficients 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; Eigenvalues and Eigenvectors; A General Method, Part I: Solving Systems with Real & Distinct or Complex Eigenvalues; A General Method, Part II: Solving Systems with Repeated Real Eigenvalues; Matrix Exponentials; Solving Linear Nonhomogeneous Systems of Equations Geometrical and Numerical Methods for First-Order Equations; An Introduction to the Phase Plane; Nonlinear Equations and Phase Plane Analysis; Bifurcations; Epidemiological Models; Models in Ecology Laplace Transforms; Introduction; Fundamentals of the Laplace Transform; The Inverse Laplace Transform; 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 Appendix A: An Introduction to MATLAB, Maple, and Mathematica; Appendix B: Selected Topics from Linear Algebra Answers to Odd Problems References Index A Review, Computer Labs, and Projects appear at the end of each chapter.
• Edition: Second edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (colour)
• Subjects: 515.352; Differential equations; Differential equations, Linear
• Languages: English
• ISBNs: 9781466509108; 9781498723695
• Related ISBNs: 9781466509085
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.