APMA 0330: Methods of Applied Mathematics I (Fall 2011)

CLASS INFORMATION

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.)

HOMEWORK, HANDOUTS AND READING SUGGESTIONS

ANNOUNCEMENTS

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

TEACHING ASSISTENT & RECITATIONS

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 FOR SOFTWARE RELATED ISSUES

Teaching Assistent	Seonmin Ahn
Email	soenmin_ahn@brown.edu
Website	Soenmin Ahn's website

COURSE DESCRIPTION

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

Short outline:

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

TEXTBOOK

Elementary Differential Equations and Boundary Value Problems , by W.E. Boyce and R.C. DiPrima , 9th ed., Wiley.

Grade

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.

Project:

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