Lecture Hours | Tuesday & Thursday 10:30–11:50 a.m. in Salomon 003 | |

Instructor | Dr. M. Chirilus-Bruckner | |

Email | martina_chirilus-bruckner@brown.edu | |

Office | Room 310 in 182 George Street | |

Phone | (401) 863 7422 | |

Office hours | Monday & Thursday 2:00–2:50 p.m. (except Thursday, Dec. 8, 2011, 9:30–10:20 a.m.) |

- FINAL EXAM: Wednesday, Dec. 14, 2012, 9:00 - 12:00 in CIT 165

Teaching Assistent | Lei Wu | |

Email | Lei_Wu@brown.edu | |

Office | Room 002 in 180 George Street | |

Office hours | Thursday, 3-5 p.m., in Room 102 in 180 George Street | |

Recitation | Wednesday, 2-4 p.m. in Room 106 in 180 George Street |

Teaching Assistent | Seonmin Ahn | |

Email | soenmin_ahn@brown.edu | |

Website | Soenmin Ahn's website |

This class provides an introduction to differential equations. They
are among the most successful mathematical modeling tools utilized in
a wide variety of applications in fields like physics, chemistry, biology, finance
and sociology. We will address the most important methods for analyzing differential equations with emphasis on finding expressions and relations for solutions analytically. Furthermore, we will discuss more powerful techniques such as qualitative analysis, numerical approximations and integral transforms.
The presented concepts are widely applicable, but will be illustrated mostly in the context of scalar first and second order ordinary differential equations (ODEs).

Prerequisite: MATH 0100

- 1. FIRST ORDER DIFFERENTIAL EQUATIONS
- Classification of differential equations
- Modeling with ODEs
- Separable equations, exact equations and integrating factors
- Linear vs nonlinear ODEs, ODE theory (existence and uniqueness)
- Qualitative analysis of ODEs
- Euler's method of numerical approximation and several improved versions
- short introduction to difference equations

- 2. SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS
- Constant coefficient equations (characteristic equation)
- Free and forced vibrations (Method of undetermined coefficients)
- Fundamental solutions and the Wronskian
- ODE theory and the Variation of Parameters Formula
- Power series solutions near ordinary points and regular singular points

- 3. LAPLACE TRANSFORM

The grade is determined as follows by homework problems, a project, two midterms, and a final exam:

Homework: | 20% |

Midterm 1: | 20% |

Midterm 2: | 20% |

Project: | 10% |

Final Exam: | 30% |

Homework problems will be handed out every Thursday and are due a week later. You can work together on homework problems, but you need to write up your solutions individually.

The project will have numerical approximations of ODEs as a topic and will involve the manipulation and usage of numerical code written in MATLAB.