**Textbook(s):**

•Boyce and Diprima, Elementary Differential Equations, 8th Edition, John Wiley and Sons, 2004, Chapters 1-7.

**CATALOG DESCRIPTION:** 20D. Introduction to
Differential Equations (4)

Ordinary differential equations: exact, separable, and linear; constant
coefficients, undetermined coefficients, variations of parameters. Systems.
Series solutions. Laplace transforms. Computing symbolic and graphical solutions
using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for
Math. 21D. Prerequisite: Math 20C (or Math 21C) with a grade of C- or better.

**LECTURES:**

Lecture |
Section(s) |
Topics Covered |

1 | 1.1-1.3 | Introduction: Mathematical modeling with ODE, Classification of ODE and PDE |

2 | 2.1 | Linear equations; Method of Integrating Factors |

3 | 2.2 | Separable Equations |

4 | 2.3,2.4 | Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations |

5 | 2.5 | Autonomous Equations and Population Dynamics |

6 | 2.6 | Exact Equations and Integrating Factors |

7 | 3.1,3.2 | Second Order Linear Equations: Fundamental Solutions of Linear Homogeneous Equations |

8 | 3.3 | Linear Independence and the Wronskian |

9 | 3.4 | Complex Roots of the Characteristic Equation |

10 | 3.5 | Repeated Roots; Reduction of Order |

Week 4 |
Midterm 1 |
TOPICS COVERED: Boyce and DiPrima 1.1-3.4. |

11 | 3.6 | Nonhomogeneous Equations; Method of Undetermined Coefficients |

12 | 3.7 | Variation of Parameters |

13 | 7.1,7.2 | Systems of First Order Linear Equations: Introduction, Review of Matrices |

14 | 7.3 | Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors |

15 | 7.4 | Basic Theory of Systems of First Order Linear Equations |

16 | 7.5 | Homogeneous Linear Systems with Constant Coefficients |

17 | 7.6 | Complex Eigenvalues |

18 | 7.7,7.8 | Fundamental Matrices, Repeated Eigenvalues |

19 | 7.9 | Nonhomogeneous Linear Systems |

20 | 5.1 | Review of Power Series; Using Power Series to Solve ODEs |

Week 8 |
Midterm 2 |
TOPICS COVERED: Boyce and DiPrima
3.5-3.7,7.1-7.9 |

21 | 5.2,5.3 | Series Solutions Near an Ordinary Point |

22 | 6.1 | The Laplace Transform: Definition of the Laplace Transform |

23 | 6.2 | Solution of Initial Value Problems |

24 | 6.3,6.4 | Step Functions; Differential Equations with Discontinuous Forcing Functions |

25 | 6.5 | Impulse Functions. |

Week 10 |
Review |
REVIEW for Final Exam |

Week 11 |
Final Exam |
TOPICS COVERED: Boyce and DiPrima 1.1-7.9. |