MATH 23 Differential Equations - Fall 2013

Course Description

Differential equations are equations that relate functions and their higher order (partial) derivatives. They provide a natural language and set of tools through which we can describe and explore the world around us.  For instance, in mathematics and physics differential equations can be used to describe the path that light will travel in exotic geometries. In engineering differential equations can be used to model how a bridge will twist under stress. And in finance, (stochastic) differential equations are used to help price financial derivatives (e.g, options, futures & credit derivatives).

This course will focus primarily on methods for obtaining exact solutions to various types of differential equations, but (as time permits) we will also explore means of ferreting out qualitative information about solutions based on the form of the differential equation. Topics will include some of the following.

• Techniques for solving first order differential equations
• The Existence and Uniqueness Theorem
• Second Order Linear Equations
• Systems of First Order Linear Equations (with an introduction to matrices)
• Power Series and Power Series Solutions to ODEs
• Fourier Series and Partial Differential Equations

Textbook

Elementary Differential Equations and Boundary Value Problems (9th Edition) by Boyce & DiPrima, Wiley 2009.

Tutorial

Tutor: Tim Dwyer

Location : Kemeny Hall 006

Time: Tue, Th, Sun 7:00pm-9:00pm

Homework

Weekly homework will be assigned every Wednesday and due on following Wednesday at the start of class. Each assignment will be divided into three parts and it is required that you hand in a separate write-up for each part. You are encouraged to collaborate with classmate, but your final write up must reflect your understanding and you must acknowledge collaborators. No late homework will be accepted.

Grading

Final grade will be computed according to the following scheme

Withdrawing

Please note that the registrar has determined that Nov. 5, 2013 is the last day to withdraw from a course (Fall 2013 Term Calendar).

Honor Principle

You are encouraged to work together on homework. However, the final writeup should be your own. On exams, all work should be entirely your own; no consultation of other persons, printed works, computing devices, or online works, or online sources is allowed without instructor's explicit permission.

Student with disabilities

Any student with a diagnosed learning disability requiring accommodations should see instructor and Ward Newmeyer (Director of Student Accessibility Services) as early in the term as possible.