Differential Equations and Linear Algebra by C. Henry Edwards

Description: About this productProduct InformationAcclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this book discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. First-Order Differential Equations; Mathematical Models and Numerical Methods; Linear Systems and Matrices; Vector Spaces; Higher-Order Linear Differential Equations; Eigenvalues and Eigenvectors; Linear Systems of Differential Equations; Matrix Exponential Methods; Nonlinear Systems and Phenomena; Laplace Transform Methods; Power Series Methods. For future math majors, engineers, or scientists that have taken two or three semesters of Calculus.Product IdentifiersPublisherPrentice Hall PTRISBN-100136054250ISBN-139780136054252eBay Product ID (ePID)71141522Product Key FeaturesFormatHardcoverPublication Year2008LanguageEnglishDimensionsWeight55.4 OzWidth8.3in.Height1.3in.Length10.1in.Additional Product FeaturesDewey Edition23Table of ContentCHAPTER 1. First-Order Differential Equations 1.1 Differential Equations and Mathematical Models 1.2 Integrals as General and Particular Solutions 1.3 Slope Fields and Solution Curves 1.4 Separable Equations and Applications 1.5 Linear First-Order Equations 1.6 Substitution Methods and Exact Equations CHAPTER 2. Mathematical Models and Numerical Methods 2.1 Population Models 2.2 Equilibrium Solutions and Stability 2.3 AccelerationVelocity Models 2.4 Numerical Approximation: Euler's Method 2.5 A Closer Look at the Euler Method 2.6 The RungeKutta Method CHAPTER 3. Linear Systems and Matrices 3.1 Introduction to Linear Systems 3.2 Matrices and Gaussian Elimination 3.3 Reduced Row-Echelon Matrices 3.4 Matrix Operations 3.5 Inverses of Matrices 3.6 Determinants 3.7 Linear Equations and Curve Fitting CHAPTER 4. Vector Spaces 4.1 The Vector Space R3 4.2 The Vector Space Rn and Subspaces 4.3 Linear Combinations and Independence of Vectors 4.4 Bases and Dimension for Vector Spaces 4.5 Row and Column Spaces 4.6 Orthogonal Vectors in Rn 4.7 General Vector Spaces CHAPTER 5. Higher-Order Linear Differential Equations 5.1 Introduction: Second-Order Linear Equations 5.2 General Solutions of Linear Equations 5.3 Homogeneous Equations with Constant Coefficients 5.4 Mechanical Vibrations 5.5 Nonhomogeneous Equations and Undetermined Coefficients 5.6 Forced Oscillations and Resonance CHAPTER 6. Eigenvalues and Eigenvectors 6.1 Introduction to Eigenvalues 6.2 Diagonalization of Matrices 6.3 Applications Involving Powers of Matrices CHAPTER 7. Linear Systems of Differential Equations 7.1 First-Order Systems and Applications 7.2 Matrices and Linear Systems 7.3 The Eigenvalue Method for Linear Systems 7.4 Second-Order Systems and Mechanical Applications 7.5 Multiple Eigenvalue Solutions 7.6 Numerical Methods for Systems CHAPTER 8. Matrix Exponential Methods 8.1 Matrix Exponentials and Linear Systems 8.2 Nonhomogeneous Linear Systems 8.3 Spectral Decomposition Methods CHAPTER 9. Nonlinear Systems and Phenomena 9.1 Stability and the Phase Plane 9.2 Linear and Almost Linear Systems 9.3 Ecological Models: Predators and Competitors 9.4 Nonlinear Mechanical Systems CHAPTER 10. Laplace Transform Methods 10.1 Laplace Transforms and Inverse Transforms 10.2 Transformation of Initial Value Problems 10.3 Translation and Partial Fractions 10.4 Derivatives, Integrals, and Products of Transforms 10.5 Periodic and Piecewise Continuous Input Functions CHAPTER 11. Power Series Methods 11.1 Introduction and Review of Power Series 11.2 Power Series Solutions 11.3 Frobenius Series Solutions 11.4 Bessel Functions References for Further Study Appendix A: Existence and Uniqueness of Solutions Appendix B: Theory of Determinants Answers to Selected Problems Index APPLICATION MODULES The modules listed here follow the indicated sections in the text. Most provide computing projects that illustrate the corresponding text sections. Maple, Mathematica, and MATLAB versions of these investigations are included in the Applications Manual that accompanies this textbook. 1.3 Computer-Generated Slope Fields and Solution Curves 1.4 The Logistic Equation 1.5 Indoor Temperature Oscillations 1.6 Computer Algebra Solutions 2.1 Logistic Modeling of Population Data 2.3 Rocket Propulsion 2.4 Implementing Euler's Method 2.5 Improved Euler Implementation 2.6 Runge-Kutta Implementation 3.2 Automated Row Operations 3.3 Automated Row Reduction 3.5 Automated Solution of Linear Systems 5.1 Plotting SecoDewey Decimal515/.35Copyright Date2010AuthorDavid E. Penney, C. Henry EdwardsEdition Number3Number of Pages792 PagesPublication Date2008-10-10

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