Differential Equations for Engineers : The Essentials

"This book surveys the broad landscape of differential equations, including elements of partial differential equations (PDEs), and concisely presents the topics of most use to engineers. It introduces each topic with a motivating application drawn from electrical, mechanical, and aerospace engineering. The text has reviews of foundations, step-by-step explanations, and sets of solved problems. It fosters students? abilities in the art of approximation and self-checking. The book addresses PDEs with and without boundary conditions, which demonstrates strong similarities with ordinary differential equations and clear illustrations of the nature of solutions. Furthermore, each chapter includes word problems and challenge problems. Several extended computing projects run throughout the text."--Provided by publisher Content: Chapter 1: Introduction1.1 Foundations1.2 Classes of Differential Equations1.3 A Few Other ThingsChapter SummarySolved ProblemsProblems to SolveWord ProblemsChallenge Problems Chapter 2: First-Order Linear Ordinary Differential Equations2.1 First Order Linear Homogeneous ODEs2.2 First Order Linear Nonhomogeneous ODEs 2.3 System Stability Chapter SummarySolved ProblemsProblems to Solve Word ProblemsChallenge Problems Chapter 3: First-Order Nonlinear Ordinary Differential Equations3.1 Nonlinear Separable ODEs3.2 The Possibility of Transforming Nonlinear Equations into Linear Ones 3.3 Successive Approximations for Almost Linear SystemsChapter SummarySolved Problems Problems to SolveWord ProblemsChallenge Problems Computing Projects: Phase 1 Chapter 4: Existence, Uniqueness, and Qualitative Analysis4.1 Motivation4.2 Successive Approximations (General Form)4.3 Existence and Uniqueness Theorem4.4 Qualitative Analysis 4.5 Stability Revisited 4.6 Local Solutions Chapter SummarySolved ProblemsProblems to SolveWord ProblemsChallenge Problems Chapter 5: Second-Order Linear Ordinary Differential Equations5.1 Second Order Linear Time-Invariant Homogeneous ODEs5.2 Fundamental Solutions5.3 Second Order Linear Nonhomogeneous ODEs5.4 Existence and Uniqueness of Solutions to Second-Order Linear ODEsChapter SummarySolved ProblemsProblems to Solve Word ProblemsChallenge Problems Chapter 6: Higher-Order Linear Ordinary Differential Equations6.1 Example: Satellite Orbit Decay6.2 Higher Order Homogeneous Linear Equations6.3 Higher Order Nonhomogeneous Linear Equations6.4 Existence and Uniqueness 6.5 Stability of Higher Order Systems Chapter SummarySolved ProblemsProblems to SolveWord ProblemsChallenge Problems Computing Projects: Phase 2 Chapter 7: Laplace Transforms7.1 Preliminaries 7.2 Introducing the Laplace Transform7.3 Laplace Transforms of Some Common Functions7.4 Laplace Transforms of Derivatives7.5 Laplace Transforms in Homogeneous ODEs7.6 Laplace Transforms in Nonhomogeneous ODEsChapter SummarySolved Problems Problems to SolveWord Problems Challenge Problems Chapter 8: Systems of First-Order Ordinary Differential Equations8.1 Preliminaries8.2 Existence and Uniqueness8.3 Numerical Integration Methods8.4 Review of Matrix Algebra8.5 Linear Systems in State Space Format8.6 A Brief Look at N-Dimensional Nonlinear Systems Chapter SummarySolved ProblemsProblems to SolveWord ProblemsChallenge Problems Chapter 9: Partial Differential Equations9.1 The Heat Equation9.2 The Wave Equation 9.3 Laplace's Equation 9.4 The Beam Equation Chapter SummarySolved Problems Problems to Solve Word ProblemsChallenge Problems The book surveys the broad landscape of differential equations, including elements of partial differential equations (PDEs). With the use of step-by-step explanations, a review of necessary foundations, and sets of solved problems, it provides concrete clarification to concepts students find abstract (e.g., eigenvalues and eigenvectors).