Schedule
This schedule and the list of topics covered may be modified slightly as the course progresses.
References are to the following texts:
"DV": Ordinary Differential Equations, Laplace Transforms
and Numerical Methods for Engineers: Notes for the course MAT 2384, by S.J. Desjardins and R. Vaillancourt (version 2012.04.23).
"K": Advanced Engineering Mathematics, 10th ed., by E. Kreyszig
| Date | Topics | References | Assignments |
| Mon, Jan 7 | Introduction to differential equations; separable equations. | DV: 1.1, 1.2. K: 1.1, 1.3. |
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| Mon, Jan 7 (Num. Meth.) | Introduction to numerical methods. Fixed point iteration | DV: 7.4. K: 19.2 |
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| Wed, Jan 9 | Homogeneous coefficients. | DV: 1.3. K: not covered |
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| Mon, Jan 14 | Exact equations | DV: 1.4. K: 1.4 |
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| Mon, Jan 14 (Num. Meth.) | Newton's method | DV: 7.5. K: 19.2 |
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| Wed, Jan 16 | Integrating factors | DV: 1.5. K: 1.4 |
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| Mon, Jan 21 | First-order linear ODEs; Bernoulli equation | DV: 1.6. K: 1.5 |
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| Mon, Jan 21 (Num. Meth.) | Newton's method, global Newton bisection method | DV: 7.5; | Wed, Jan 23 | Second-order linear homogeneous ODEs; constant coefficients | DV: 2.1,2.2. K: 2.1, 2.2, 2.3 |
Assignment 1 (Solutions) |
| Mon, Jan 28 | Second-order linear ODEs, including Euler-Cauchy | DV: 2.3-2.6. K: 2.4-2.6 |
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| Mon, Jan 28 (Num. Meth.) | Lagrangian interpolation | DV: 8.1. K: 19.3 |
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| Wed, Jan 30 | (More 2nd order); Linear ODEs of arbitrary order | DV: 3.1. K: 3.1, 3.2 |
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| Mon, Feb 4 | Linear ODEs of arbitrary order | DV: 3.2-3.3. K: 3.2, 3.3 |
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| Mon, Feb 4 (Num. Meth.) | Newton's Divided Difference interpolation | DV: 8.2. K: 19.3 |
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| Wed, Feb 6 | Method of undetermined coefficients, forced oscillations | DV: 3.4, 3.6. K: 2.7, 2.8, 2.9 |
Assignment 2 (Solutions) |
| Mon, Feb 11 | Variation of parameters | DV: 3.5. K: 2.10 |
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| Mon, Feb 11 (Num. Meth.) | Cubic Splines | DV: 8.6; K: 19.3 |
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| Wed, Feb 13 | [no lecture due to snow] | ||
| Feb 17–23 | |||
| Mon, Feb 25 | Variation of parameters (cont.) | DV: 3.5. K: 2.10 |
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| Mon, Feb 25 (Num. Meth.) | Numerical integration: Midpoint, trapezoidal, Simpson | DV: 9.4-9.7; K: 19.5 |
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| Wed, Feb 27 | Systems of ODEs | DV: 4.1, 4.2. K:4.1, 4.2, 4.4 |
Assignment 3 (Solutions) |
| Mon, Mar 4 | MIDTERM (first and last pages here) Solutions | ||
| Mon, Mar 4 (Num. Meth.) | More numerical integration, including Gaussian quadrature | DV: 9.10; K: 19.5; Gaussian integration handout |
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| Wed, Mar 6 | Fundamental systems; Homogeneous linear systems with constant coefficients | DV: 4.3, 4.4. K: 4.2, 4.3 |
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| Mon, Mar 11 | Nonhomogeneous Linear Systems | DV: 4.5. K: 4.6 |
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| Mon, Mar 11 (Num. Meth.) | Numerical solution of ODEs. Euler's method | DV: 10.1, 10.2; K: 21.1 |
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| Wed, Mar 13 | Laplace transforms: introduction | DV: 5.1, 5.2 | |
| Mon, Mar 18 | Laplace transforms: first shifting | DV: 5.3 | Assignment 4 (Solutions) |
| Mon, Mar 18 (Num. Meth.) | Improved Euler's method | DV: 10.2 | |
| Wed, Mar 20 | Laplace transforms: second shifting; Dirac delta function | DV: 5.3, 5.4 | |
| Mon, Mar 25 | Laplace transforms: derivatives | DV: 5.5, 5.6 | |
| Mon, Mar 25 (Num. Meth.) | Runge-Kutta methods | DV: 10.3 | |
| Wed, Mar 27 | Laplace transforms: convolution | DV: 5.7 | |
| Mon, Apr 1 | Power series solutions | DV: 6.1, 6.2 | |
| Mon, Apr 1 (Num. Meth.) | TBD | ||
| Wed, Apr 3 (last lecture) | Power series solutions | DV: 6.2, 6.3 | Assignment 5 (Solutions) |
| Mon, April 24 | FINAL EXAM (first and last pages here) | ||