Differential Equations (Classic Version)

Chapter 1: Introduction to Differential Equations <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Differential Equation Models. The Derivative. Integration.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 2:&nbsp; First-Order Equations <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Project 2.10 The Daredevil Skydiver.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 3: Modeling and Applications <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 4: Second-Order Equations <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 5: The Laplace Transform <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace Transform</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 6: Numerical Methods <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Euler’s Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Project 6.6 Numerical Error Comparison.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> Chapter 7: Matrix Algebra <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Chapter 8: &nbsp;An Introduction to Systems</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Definitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Chapter 9: &nbsp;Linear Systems with Constant Coefficients</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Chapter 10: Nonlinear Systems</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator—Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Chapter 11: Series Solutions to Differential Equations</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">Review of Power Series. Series Solutions Near Ordinary Points. Legendre’s Equation. Types of Singular Points–Euler’s Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points – the General Case. Bessel’s Equation and Bessel Functions.</p> <p style="MARGIN: 0in 0in 0pt; mso-pagination: none; mso-layout-grid-align: none" sonormal="">&nbsp;</p> <p style="MARGIN: 0in 0in 0pt" sonormal="">&nbsp;</p>