Welcome toDifferential Equations |
Representations of solutions to the system of de's: x' = y, and y' = -x. |
Welcome toDifferential Equations |
Representations of solutions to the system of de's: x' = y, and y' = -x. |
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Description of Notes Contents: |
| Introduction | Illustrates differential equations, initial value problems, and their solutions |
| General and particular solutions | Shows the difference between general and particular solutions |
| Direction fields and solution curves | Demonstrates the use of Maple to draw slope fields and solution curves |
| Sample Maple code | Uses Maple to obtain partial fractions decompositions, solve initial value problems, and evaluate indefinite integrals |
| Euler's method | Introduces numerical methods. Discusses conditioning and illustrates with examples. |
| Linear Independence and the Wronskian | Defines linear dependence/independence and the Wronskian, and illustrates the use of Maple to calculate the Wronskian. |
| Graphing solutions of systems of differential equations | Shows phase portraits, time series graphs, and space curves |
| Euler's method for systems of differential equations | Shows how to convert a second order d.e. to a first order system, solve using Euler's method, then generate graphs of phase portrait, time series plots, and a space curve |
| Eigenvalue method | Shows how to solve a linear system of differential equations using the eigenvalue method. Examples include real valued and complex valued eigenvalues (non repeated). |
| Introduction to Laplace Transforms | Covers definition of Laplace transform, examples, built-in Laplace transform commands, sectionally continuous functions and exponential order |
| Example Laplace solutions | Illustrates use of Laplace transforms to obtain the solution of a 2nd order ode with initial conditions, and a 1st order system with initial conditions. |
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