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Exam 1 Notes |
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| 1 |
Introduction. Solutions of some differential equations. Separable equations. |  |
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| 1 | Method of Integrating Factors (section 2.1) |
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| 1 | Modelling with first order equations, Direction field, Autonomous equations, and population dynamics. | |
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| 1 | Differences between Linear and Nonlinear Equations (section 2.4) | |
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| 1 | Exact Equation and Integrating Factor (Section 2.6) |
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| 2 | Solutions of linear homogeneous equations of second order. The Wronskian.(Section 3.2) |
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| 2 | Homogeneous Equations with Constant Coefficients.(Section 3.1) |
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Exam 2 Notes
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| 2 | Complex Numbers Review |
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| 2 | Complex Numbers Worksheet |
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| 2 | Complex Roots of the Characteristic Equation (section 3.3) |
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| 2 | The case of repeated roots (section 3.4) |
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| 2 | Reduction of order (Section 3.4 ) |
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| 2 | Nonhomogeneous Equations. Method of Undetermined Coefficients (section 3.5) |
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| 3 | Method Variation of Parameters (section 3.6) |
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| 3 | Mechanical and Electrical Vibrations (section 3.7) |
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| 3 | Forced Vibrations (section 3.8) |
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| 3 | Laplace Transform: definition and solution of IVP (sections 6.1-6.2) |
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New material for Final Exam
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4
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Step functions. Differential equations with discontinuous forcing functions (sections 6.3 and 6.4). |
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4
| Impulse functions (section 6.5 ). The convolution integral.(section 6.6) |
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4
| Systems of FIRST Order Equations. Preliminaries. |
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4
| Appendix: Matrices and Matrix Multiplication. |
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4
| Basic Theory of Systems of First Order Linear Equations (sec. 7.4) |
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5
| Systems of Linear Algebraic Equations. Eigenvalues and Eigenvectors (section 7.3) |
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| Homogeneous Linear Systems with Constant Coefficients (sec. 7.5) |
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| Complex Eigenvalues (sec.7.6) |
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| Repeated Eigenvalues |
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5
| Non-homogeneous Linear Systems (section 7.9) |
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5
| The Phase Plane: Linear Systems (section 9.1) |
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