| Math 421 is directed at students in the Chemical and Biochemical Engineering (155) and the Mechanical & Aerospace curriculum (650). It is designed to help these students prepare for upper-level engineering courses. The course has three parts: | ||
|
(6 lectures) The definition, simple properties, and applications to the solution of ODE's. |
(13 lectures) Orthogonal expansions; Fourier series; Fourier sine and cosine series; Sturm-Liouville problems; the wave and heat equations in 1 and 2 space dimensions. |
(7 lectures) Math 421 students are assumed to have some background in linear algebra in two and three dimensions. This part of the course is a fast-paced treatment of matrices and vectors of any size. The aim is to insure that important facts and algorithms are clearly stated and can be used by students in later courses. |
We will cover selected sections from Chapters 3, 4, 8, 12, 13, and 14 of the
text that treat the topics mentioned above.
| Date | Section | Topics | Homework problems (* = graded) | Date due |
|---|---|---|---|---|
| 1/21 | 4.1 | Definition of the Laplace transform | 1, 5*, 7*, 13, 23, 25, 31, 35, 37 | 1/26 |
| 4.2.1 | Inverse Laplace Transform | 7, 11, 23* | 1/26 | |
| 1/26 | 4.2.2 | Laplace Transform of Derivatives (Quiz) | 31*, 35*, 39 | 2/02 |
| 1/28 | 4.3 | Translation Theorems | 3, 7, 9, 11, 15*, 19, 37, 41, 45, 47, 49-54, 63*, 67 | 2/02 |
| 2/02 | 4.4.1 | Derivatives of Transforms | 3, 7, 11*, 13 | 2/09 |
| 4.4.2 | Transforms of Integrals (Quiz) | 19, 27*, 33, 37*, 39 | 2/09 | |
| 2/04 | 4.4.3 | Transforms of a Periodic Function | 49*, 51* | 2/09 |
| 4.5 | Dirac Delta Function | 1, 3, 9* | 2/09 | |
| 2/09 | 4.6 | Systems of Linear Differential Equations (Quiz) | 1, 7, 9*, 11* | 2/16 |
| 2/11 | 12.1 | Orthogonal Functions | 1, 3*, 7, 13*, 15, 16, 17, 21 | 2/16 |
| 2/16 | 12.2 | Fourier Series (Quiz) | 1, 3, 5*, 9*, 15, 17*, 19, 21 | 2/23 |
| 2/18 | Catch up and review | |||
| 2/23 | First midterm exam (closed book) | |||
| 2/25 | 12.3 | Fourier Sine and Cosine Series | 1, 3, 5, 7, 13, 19*, 23, 29*, 41* | 3/02 |
| 3/02 | 12.4 | Complex Fourier Series and Frequency Spectrum | 1, 5*, 7 | 3/09 |
| 12.5 | Regular Sturm-Liouville Problems (Quiz) | 1*, 5 | 3/09 | |
| 3/04 | 13.1 | Separable Partial Differential Equations | 1, 3* | 3/09 |
| 13.2 | Classical Equations and Boundary-Value Problems | 1, 3, 5*, 7, 9*, 11 | 3/09 | |
| 3/09 | 3.9 | Linear Models: Boundary-Value Problems | 9, 13, 15 | 3/23 |
| 13.3 | Heat Equation (Quiz) | 1*, 3*, 5 | 3/23 | |
| 3/11 | 13.4 | Wave Equation | 1*, 3, 5, 13, 15* | 3/23 |
| Spring break | ||||
| 3/23 | 13.5 | Laplace's Equation (Quiz) | 1, 3, 5*, 7*, 15* | 3/30 |
| 3/25 | 13.6 | Nonhomogeneous Boundary Value Problems | 1*, 3, 5* | 3/30 |
| 3/30 | 13.7 | Orthogonal Series Expansions | 1* | 4/06 |
| 13.8 | Fourier Series in Two Variables (Quiz) | 1*, 3* | 4/06 | |
| 4/01 | 14.1 | Laplace's Equation in Polar Coordinates | 1*, 3*, 7* | 4/06 |
| 4/06 | Catch up and review | |||
| 4/08 | Second midterm exam (closed book) | |||
| 4/13 | 8.1 | Matrix Algebra | 15, 17, 19*, 23, 29, 35, 37, 39, 46* | 4/20 |
| 8.2 | Systems of Linear Algebraic Equations | 5, 9*, 11, 15*, 27, 39, 41* | 4/20 | |
| 4/15 | 7.6 | Vector Spaces | 11, 13, 17, 27* | 4/20 |
| 8.3 | Rank of a Matrix | 1, 5, 7*, 13*, 15, 17 | 4/20 | |
| 4/20 | 8.4 | Determinants | 19, 21, 25*, 27, 29 | 4/27 |
| 8.5 | Properties of Determinants (Quiz) | 1, 3, 5, 7, 9, 11, 13*, 15, 21, 23, 31, 33* | 4/27 | |
| 4/22 | 8.6 | Inverse of a Matrix | 5, 7, 19, 21, 25*, 27, 31, 43, 51, 53 | 4/27 |
| 8.7 | Cramer's Rule | 1, 9, 11* | 4/27 | |
| 4/27 | 8.8 | Eigenvalue Problem (Quiz) | 5, 13*, 19 | 5/04 |
| 4/29 | 8.10 | Orthogonal Matrices | 7, 13*, 15 | 5/04 |
| 8.12 | Diagonalization of Matrices | 5, 13*, 21, 25, 27, 37*, 39 | 5/04 | |
| 5/04 | Catch up and review | |||
| 5/07 | 8:00 - 11:00 am (room SEC 204) Final exam (closed book) | |||
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