#### Syllabus and Homework Problems for Math 421-Section 04 (Fall 2010)

**Instructor:**Prof. Roe Goodman tel. (732) 445-2390 ext. 3071**When and where:**Tuesday 10:20 - 11:40 am, SEC-206 BUS and Friday 10:20 - 11:40 am, SEC-204 BUS (**two rooms**)**Office hours:**Monday and Wednesday 2:00 - 3:00 pm, Hill 428 (by appointment at other times)**Text:***Advanced Engineering Mathematics*(fourth edition) by Dennis G. Zill and Warren S. Wright

**Notes:** The syllabus and homework problems may be revised during the term. Be sure to load the latest version into your browser.

The parts of the fourth edition of the text (and the numbering of the homework problems) used in the course are identical (except for numbering of theorems and the colors in printing) to the corresponding parts of the third edition.

**Important:** The selection of graded homework problems and the dates due were revised October 10. Be sure to submit the correct problems on the indicated dates.

Session Date | Section | Topics (Quiz on previous two lectures) | Homework problems (* = hand in for grading) | Date due |
---|---|---|---|---|

#1 9/03 |
4.1 | Definition of the Laplace transform | 1, 3, 5, 7*, 13, 23*, 25, 29, 31, 35, 37, 39, 41 | 9/14 |

#2 9/07 |
4.2.1 | Inverse Laplace Transform | 7, 8*, 11, 15, 17, 18*, 23 | 9/14 |

4.2.2 | Laplace Transform of Derivatives Linear Differential Equations |
31, 32*, 35, 38* | 9/14 | |

#3 9/10 |
4.3 | Translation Theorems Unit Step Function (Heaviside Function) (Quiz) |
3, 7, 9, 11, 15, 19*, 24*, 40*, 41, 45, 47, 49-54, 55, 63*, 67 | 9/14 |

#4 9/14 |
4.4.1 | Derivatives of Transforms | 3, 7, 8*, 11*, 13, 14* | 9/21 |

4.4.2 | Transforms of Integrals; Convolution Volterra Integral Equation |
19, 22, 25, 27*, 33, 37*, 39* | 9/21 | |

#5 9/17 |
4.4.3 | Transforms of a Periodic Function | 49*, 51*, 52 | 9/21 |

4.5 | Dirac Delta Function Impulse Response Function (Quiz) |
1, 2*, 3, 5, 9* | 9/21 | |

#6 9/21 |
4.6 | Systems of Linear Differential Equations | 1, 2*, 7, 9*, 11* | 9/28 |

#7 9/24 |
7.6 | Vector Spaces | 11, 13, 17, 27*, 28* | 9/28 |

8.1 | Matrix Algebra | 15, 17, 19*, 23*, 29, 35, 37, 39 | 9/28 | |

8.2 | Systems of Linear Algebraic Equations (Quiz) |
5, 9*, 11, 15*, 17* | 9/28 | |

#8 9/28 |
8.3 | Rank of a Matrix | 1, 5, 7*, 13*, 15, 17 | 10/05 |

8.4 | Determinants | 15, 19, 21, 25*, 27, 29 | 10/05 | |

8.5 | Properties of Determinants | 1, 3, 5, 7, 9, 11, 13*, 15, 21, 23*, 31, 33* | 10/05 | |

#9 10/01 |
8.6 | Inverse of a Matrix | 5, 7*, 19, 23*, 27, 31, 43, 51*, 53 | 10/05 |

8.7 | Cramer's Rule (Quiz) |
1, 9, 11* | 10/05 | |

#10 10/05 |
8.8 | Eigenvalue Problem | 3, 5, 13*, 15*, 21* | 10/12 |

#11 10/08 |
8.10 | Orthogonal Matrices | 1*, 5, 7, 13, 15* | 10/12 |

8.12 | Diagonalization of Matrices (Quiz) |
3*, 5*, 13*, 21, 25, 27, 37*, 38, 39* | 10/12 | |

#12 10/12 |
Catch up and review | |||

#13 10/15 |
First midterm exam on Chapter 4 and Chapter 8 (sections 1-8, 10, and 12) (closed book - Laplace transform formula page provided) |
|||

#14 10/19 |
12.1 | Orthogonal Sets of Functions | 1, 3*, 5*, 7, 8*, 9, 12, 15, 16, 17, 18*, 21 | 10/26 |

12.2 | Fourier Series | 1*, 2, 3*, 5*, 7, 9* | 10/26 | |

#15 10/22 |
12.2 | Convergence of Fourier Series (Quiz) |
11, 13, 17*, 19, 20*, 21 | 10/26 |

#16 10/26 |
12.3 | Fourier Sine and Cosine Series Half range expansions |
1, 3, 5, 7, 13*, 14*, 19, 25*, 27, 29*, 41* | 11/02 |

12.4 | Complex Fourier Series | 1*, 3*, 5*, 11, 12 | 11/02 | |

#17 10/29 |
3.9 | Example 2: Boundary Value Problems (BVP) | 9, 11* | 11/02 |

12.5 | Regular Sturm-Liouville Problems (Quiz) |
1*, 5 | 11/02 | |

#18 11/02 |
13.1 | Separable Partial Differential Equations | 1*, 3*, 9* | 11/09 |

#19 11/05 |
13.2 | Heat Equation and BVP | 1, 3*, 5*, 9* | 11/09 |

13.3 | Solution to BVP for Heat Equation (Quiz) |
1*, 2*, 3*, 4* | 11/09 | |

#20 11/09 |
13.2 | Wave Equation and BVP | 7, 8 | |

13.4 | Solution to BVP for Wave Equation | 1*, 2*, 5*, 8*, 11* | 11/16 | |

#21 11/12 |
13.2 | Laplace Equation and BVP | 11 | |

13.5 | Solution to Laplace's Equation in a Rectangle (Quiz) |
1*, 3, 4* | 11/16 | |

#22 11/16 |
13.5 | Dirichlet problem for Laplace's Equation in a Rectangle | 5*, 7*, 15* | 11/30 |

#23 11/19 |
Second midterm exam on Chapter 12 (sections 1-5) and Chapter 13 (sections 1-5) (closed book - formula page provided) |
|||

#24 11/23 |
13.6 | Nonhomogeneous BVP | 1*, 5* | 11/30 |

#25 11/30 |
13.7 | Orthogonal Series Expansions for BVP | 1*, 5* | 12/07 |

#26 12/03 |
13.8 | Fourier Series in Two Variables (Quiz) |
1*, 3*, 5* | 12/07 |

#27 12/07 |
14.1 | Laplace's Equation in Polar Coordinates Steady Temperatures in Circular Plates |
1*, 3*, 7* | 12/10 |

#28 12/10 |
Catch up and review | |||

12/16 | 12:00 - 3:00 pm (room TBA) Final exam (closed book - formula page provided) |