The text is Advanced Engineering Mathematics (fifth
edition) by Peter V. O'Neil. It is published by Brooks/Cole, 2003 and
has 1236+82[Answers]+9[Index] pages (ISBN# 0-534-40077-9).
| ||

Each entry in the table below represents
approximately 1 lecture. | ||

Laplace transformsThe definition and applications to the solution of ODE's. |
Linear algebra421 students are assumed to have some background in linear
algebra. Therefore part of this is a fast-paced review, combined with an effort to insure
that important facts and algorithms are clearly stated and can be used by
students in later courses. |
Fourier series and some classical
boundary value problemsFourier sine and cosine series; the wave and heat equations in 1 and 2 space dimensions. |

Section(s)
of text |
Section title(s) | Suggested problems |
---|---|---|

3.1 | Def'n of Laplace transform and basic properties | 3, 5, 7, 13, 15, 17, 27, 29. |

3.2 | Solution of initial value problems using the Laplace transform | 3, 5, 7, 9. |

3.3 | Shifting theorems and the Heaviside function | 1, 3, 7, 9, 13, 15, 17, 19, 21, 25, 31, 37, 47, 49. |

3.4 | Convolution | 1, 3, 7, 9, 11, 13, 17, 19, 23. |

3.5 | Unit impulses and the Dirac delta function | 1, 3, 7, 9, 13, 19. |

3.6 | Laplace transform solution of systems | 1, 3, 5, 7, 9, 11, 15. |

3.7 | Differential equations with polynomial coefficients | 1, 3, 7, 11. |

5.4 5.5 |
The vector space R^n Linear independence, spanning sets, and dimension in R^n | 1, 7, 9, 14, 15, 19, 26. 1, 2, 5, 17, 19, 21 |

6.1 | Matrices | 10, 21, 27, 28, 29 |

6.3 6.4 |
Row echelon form of a matrix Row & column spaces of a matrix and rank | 1, 3, 9. 1, 3, 9. |

6.5 | Solution of a homogeneous system of linear equations | 1, 5, 13. |

6.7 | Nonhomogeneous systems of linear equations | 1, 5, 9. |

6.9 | Matrix inverses | 1, 7, 13. |

7.1 7.2 7.3 7.4 |
Permutations Definition of determinant Properties of determinant Evaluation of determinant by elementary row & column ops. | 1, 7 |

7.5 7.6 |
Cofactor expansions Determinants of triangular matrices | 5, 13, 19 a, b. 1 |

7.7 7.8 |
Determinant formula for matrix inverse Cramer's Rule | 1, 7. 1, 5, 9. |

8.1 | Eigenvalues and eigenvectors | 1 a, b, 7 a, b, 19 a, b. |

8.2 | Diagonalization of matrices | 1, 7 |

13.1 13.2 |
Why Fourier series? The Fourier series of a function |
1 1, 5, 7, 9, 11. |

13.4 | Fourier cosine and sine series | 1, 3, 5, 7. |

13.5 | Integration and differentiation of Fourier series | 3, 5. |

16.1 16.2 |
The wave equation and initial and boundary conditions Fourier series solution of the wave equation |
1, 3. 1, 3, 5, 9. |

16.2 16.4 |
Fourier series and d'Alembert solutions of the wave equation |
1, 3, 5, 11, 13, 17. |

16.7 | Vibrations of a rectangular membraneNot covered in this class! |
1, 3. |

17.1 17.2 |
The heat equation and initial and boundary conditions Fourier series solution of the heat equation |
1, 2, 3. 1, 3, 7, 9, 11. |

17.2 17.5 |
Heat conduction on a rectangular plate Not covered in this class! |
7, 13, 15. 3 |