Differential Equations Computing And Modeling 4Th Edition Pdf - Download Free Apps
Chapter 1
First-Order Differential Equations
REVIEW OF DIFFERENTIATION. BRIEF TABLE OF INTEGRALS 1. 1,1 1 n udu Cnn u n 2. 1 du u Cln u 3. Edu e Cuu uu4. SEVENTH EDITION DIFFERENTIAL EQUATIONS with Boundary-Value Problems DENNIS G. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS 82.
| 1.1 | Differential Equations and Mathematical Methods | Problems | p.8 |
| 1.2 | Integrals as General and Particular Solutions | Problems | p.17 |
| 1.3 | Slope Fields and Solution Curves | Problems | p.27 |
| 1.4 | Separable Equations and Applications | Problems | p.43 |
| 1.5 | Linear First-Order Equations | Problems | p.56 |
| 1.6 | Substitution Methods and Exact Equations | Problems | p.74 |
| Review Problems | p.78 |
Chapter 2
Differential Equation
Mathematical Models And Numerical Methods
| 2.1 | Population Models | Problems | p.87 |
| 2.2 | Equilibrium Solutions and Stability | Problems | p.98 |
| 2.3 | Acceleration-Velocity Models | Problems | p.108 |
| 2.4 | Numerical Approximation: Euler's Method | Problems | p.121 |
| 2.5 | A Closer Look at the Euler Method | Problems | p.132 |
| 2.6 | The Runge-Kutta Method | Problems | p.142 |
Chapter 3
Linear Equations Of Higher Order
| 3.1 | Introduction: Second-Order Linear Equations | Problems | p.158 |
| 3.2 | General Solutions of Linear Equations | Problems | p.170 |
| 3.3 | Homogeneous Equations with Constant Coefficients | Problems | p.183 |
| 3.4 | Mechanical Vibrations | Problems | p.195 |
| 3.5 | Nonhomogeneous Equations and Undetermined Coeffcients | Problems | p.210 |
| 3.6 | Forced Oscillations and Resonance | Problems | p.222 |
| 3.7 | Electrical Circuits | Problems | p.231 |
| 3.8 | Endpoint Problems and Eigenvalues | Problems | p.244 |
Chapter 4
Introduction To Systems Of Differential Equations
| 4.1 | First-Order Systems of Applications | Problems | p.255 |
| 4.2 | The Method of Elimination | Problems | p.266 |
| 4.3 | Numerical Methods for Systems | Problems | p.279 |
Chapter 5
Linear Systems Of Differential Equations
| 5.1 | Matrices and Linear Systems | Problems | p.301 |
| 5.2 | The Eigenvalue Method for Homogeneous Systems | Problems | p.316 |
| 5.3 | Second-Order Systems and Mechanical Applications | Problems | p.328 |
| 5.4 | Multiple Eigenvalue Solutions | Problems | p.345 |
| 5.5 | Matrix Exponentials and Linear Systems | Problems | p.359 |
| 5.6 | Nonhomogeneous Linear Systems | Problems | p.369 |
Chapter 6
Nonlinear Systems And Phenomena
| 6.1 | Stability and the Phase Plane | Problems | p.381 |
| 6.2 | Linear and Almost Linear Systems | Problems | p.395 |
| 6.3 | Ecological Models: Predators and Competitors | Problems | p.408 |
| 6.4 | Nonlinear Mechanical Systems | Problems | p.424 |
Chapter 7
Laplace Transform Methods
| 7.1 | Laplace Transforms and Inverse Transforms | Problems | p.450 |
| 7.2 | Transformation of Initial Value Problems | Problems | p.462 |
| 7.3 | Translation and Partial Fractions | Problems | p.472 |
| 7.4 | Derivatives, Integrals, and Products of Transforms | Problems | p.481 |
| 7.5 | Periodic and Piecewise Continuous Input Functions | Problems | p.491 |
| 7.6 | Impulses and Delta Functions | Problems | p.502 |