Differential Equations : First and Second Order Linear Differential Equations.

Cover -- Differential Equations: First and Second Order Linear Differential Equations -- Contents -- Abbreviations Used in this Book -- CHAPTER 1: Definition of Terms and Review of Linear Algebra -- 1.1 Basic Definitions -- 1.1.1 What Is a Differential Equation? -- 1.1.2 Solution to a Differential Equation -- 1.1.3 Family of Solutions -- 1.1.4 Direction Fields -- 1.2 Some Linear Algebra -- 1.2.1 Matrices -- 1.2.2 Systems of Linear Equations -- 1.2.3 Matrix Addition and Subtraction and Scalar Product -- 1.2.4 Transpose of a Matrix -- 1.2.5 Dot Product and Matrix Multiplication -- 1.2.6 Determinants -- 1.2.7 The Inverse of a Square Matrix -- 1.2.8 Matrix Form of a System of Linear Equations -- 1.2.9 Linear Dependence -- 1.2.10 Eigenvalues and Eigenvectors -- 1.2.11 Diagonalization -- CHAPTER 2: Linear First Order Differential Equations -- 2.1 Linear First Order DE -- 2.1.1 Bernoulli Differential Equation -- 2.2 Separable Differential Equations -- 2.3 Exact Differential Equations -- 2.4 Homogeneous Differential Equations -- 2.5 Existence and Uniqueness -- CHAPTER 3: Homogeneous Second Order Differential Equations -- 3.1 Linear Homogeneous DE -- 3.2 Linear Independence and the Wronskian -- 3.2.1 Linear Independence -- 3.2.2 The Wronskian -- 3.3 Solving ay" + by' + cy = g(x) -- 3.3.1 The Method of Undetermined Coefficients -- 3.3.2 Variation of Parameters -- Bibliography -- Index -- Back Cover.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.