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Exam 1 Notes
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Notes with spaces
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1
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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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Differences between Linear and Nonlinear Equations (section 2.4) |
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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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Homogeneous Equations with Constant Coefficients.(Section 3.1) |
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Exam 2 Notes
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Notes without spaces
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Notes with spaces
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2 |
Complex Numbers Review
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2
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Complex Numbers Worksheet
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2
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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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Notes without spaces
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Notes with spaces
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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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5
| Homogeneous Linear Systems with Constant Coefficients (sec. 7.5)
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5
| Complex Eigenvalues (sec.7.6)
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5
| 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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