Differential Equations and Linear Algebra, Global Edition, 4th Edition
- Length: 757 pages
- Edition: 4
- Language: English
- Publisher: Pearson
- Publication Date: 2020-07-08
- ISBN-10: 1292356952
- ISBN-13: 9781292356952
- Sales Rank: #0 (See Top 100 Books)
For courses in Differential Equations and Linear Algebra.
The right balance between concepts, visualisation, applications, and skills
Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena – a comprehensive approach that makes accessible a wider range of more realistic applications.
The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.
Cover Title Page Copyright Page Contents Application Modules Preface CHAPTER 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 Acceleration-Velocity Models 2.4 Numerical Approximation: Euler's Method 2.5 A Closer Look at the Euler Method 2.6 The Runge–Kutta 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 A Gallery of Solution Curves of Linear Systems 7.5 Second-Order Systems and Mechanical Applications 7.6 Multiple Eigenvalue Solutions 7.7 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 A B C D E F G H I J K L M N O P Q R S T U V W Z Table of Integrals
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