لایب سان

• ISBN-10 : 1292356952
• ISBN-13 : 978-1292356952

9781292356983 1292356987

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

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