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Notes |
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| EXAM 1 |
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| January 13 |
Introduction, Solutions of some differential equations, Separable equations Notes without space Partially Completed Notes |
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| January 17 |
Method of Integrating Factors Notes without space Notes with space |
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| January 22 |
Modelling with first order equations, Direction field, Autonomous equations, and population dynamics Notes without space Notes with space Partially Completed Notes | ||||
| January 28 |
Differences between Linear and Nonlinear Equations (section 2.4) Notes without space Notes with space Partially Completed Notes | ||||
| January 30 |
Exact Equation and Integrating Factor (Section 2.6) Notes without space Notes with space | ||||
| February 3 | Solutions of linear homogeneous equations of second order. The Wronskian. Notes without space Notes with space Partially Completed Notes | ||||
| February 5 |
Homogeneous Equations with Constant Coefficients. Notes without space Notes with space Partially Completed Notes |
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February 10
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Complex Numbers Review and Worksheet | ||||
| Complex Roots of the Characteristic Equation Notes without space Notes with space Completed Notes |
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| February 14 | The case of repeated roots (section 3.4) Notes without space Notes with space |
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| February 18 | Reduction of order (Section 3.4 continued) Notes without space | ||||
| February 21 |
Nonhomogeneous Equations. Method of Undetermined Coefficients (section 3.5) Notes without space Notes with space Partially Completed Notes |
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| February 23 | Method Variation of Parameters (section 3.6) Notes without space Notes with space |
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| February 25 | Mechanical and Electrical Vibrations (section 3.7)Notes without space Notes with space Completed Notes |
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February 28
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Forced Vibrations (section 3.8) Notes without space | ||||
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March 03
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March 16
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Step functions. Differential equations with discontinuous forcing functions (sections 6.3 and 6.4). Notes without space Notes with space | ||||
| Impulse functions (section 6.5 ); The convolution integral.(section 6.6) Notes without space Notes with space Partially Completed Notes |
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| March 24 |
Systems of FIRST Order Equations. Preliminaries. Notes without space Appendix: Matrices and Matrix Multiplication. Notes without space Partially Completed Notes |
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| April 2 | Basic Theory of Systems of First Order Linear Equations (sec. 7.4) Notes without space | ||||
| Systems of Linear Algebraic Equations. Eigenvalues and Eigenvectors (section 7.3) Notes without space Partially Completed Notes |
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| Homogeneous Linear Systems with Constant Coefficients (sec. 7.5) Notes without space Partially Completed Notes |
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| April 11 |
Complex Eigenvalues (sec.7.6) Notes without space Partially Completed Notes |
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| Repeated Eigenvalues Notes without space Notes with space Partially Completed Notes |
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| New Material for Final Exam | |||||
| April 18 | Non-homogeneous Linear Systems (section 7.9) Notes without space Notes with space Completed Notes |
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| The Phase Plane: Linear Systems (section 9.1) Notes without space Notes with space |
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| April 22 |
Power Series, Taylor Series and Analytic Functions (section 5.1) Notes with space |
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| Series of Solutions near an Ordinary Point (sections 5.2 and 5.3)Notes with space Partially Completed Notes |
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