Math 23: Differential Equations

This version was revised on March 18, 2010.

Course Description
This course is a survey of important types of differential equations, both linear nad nonlinear, which often occur in sciences, engineering, medicine and economics. Topics include the study of systems of ordinary differential equations using eigenvectors and eigen values, analytical and numerical solutions of first and second order equations, and using Fourier series to solve for elementary partial differential equations.

Prerequisites: Calculus of Vector-Valued Functions (Math 13)

Elementary differential equations and boundary value problems
Ninth Edition,
by William E. Boyce and Richard C. DiPrima.

	Section 2 (CRN 32601)	Section 1 (CRN 30066)
Instructor	Craig Sutton	Meifang Chu
Lecture Time/Room	MWF 12:30 - 1:35 Kemeny 007	MWF 10:00-11:05 Kemeny 105
X-hour	Tuesdays 13:00-13:50	Thursdays 12:00-12:50
Office hours	Wednesdays 14:00-15:00 Thursdays 14:00-15:30	Thursdays 13:00-14:20 Fridays 13:05-14:20
Office	321 Kemeny	245 Wilder
Tel	646-1059	646-2971
Email	craig.sutton@dartmouth.edu	meifang.chu@dartmouth.edu

Grades will be based on
(1) Weekly Homework: 15%, (2) Two Midterm Exams: 25% each, (3) Final Exam: 35%

Exams:
There will be two mid-term exams, a final exam and no quizzes.
Midterm I : Wednesday, April 21, 6:00-8:30pm. Location: Carpenter 013
Midterm II: Wednesday, May 12, 6:00-8:30pm. Location: Carpenter 013
Final: Friday, June 4, 11:30am-2:30pm. Location: TBD.

Homework
Homework will be assigned weekly. Each homework must be submitted at the beginning of the class on the following Mondays. Late homework will not be accepted. Both sections will have the same homework assignments and exam papers but each instructor may post different course materials on the Dartmouth Blackboard. Some of the problem sets will require using the given Matlab codes to generate numerical results and graphics. For access to Matlab, please check the Dartmouth Computing website http://www.dartmouth.edu/comp/soft-comp/software/research/packages/matlabdownload.html.

Honor Code
Collaboration and discussion of general ideas related to homework problems are allowed and encouraged but you must write down the solutions by yourself in your own words; No collaboration is permitted on exams.

Free Tutorials
Three times a week Katherine Kinnaird and Kassie Archer, who are graduate students in mathematics, will run the tutorials for Math 23. Participation in these tutorials is highly recommended.
Time: Sunday, Tuesday, Thursday at 7-9 PM from April 20 to June 1.
Location: Kemeny 007. (note: on April 8th it will be in Carson L01)

Private Tutoring
Tutor Clearinghouse may have private one-on-one tutors available for Math 23. If you receive financial aid, the College will pay for three hours of tutoring per week. If you would like to have a tutor, please go to 301 Collis and fill out an application.

Religious Observance
If you have a religious observance that conflicts with your participation in the course, please meet with the instructor before the end of the second week of the term to discuss appropriate accommodations.

Students with Disabilities
Students with disabilities who will be taking this course and may need disability related classroom accommodations are encouraged to make an appointment to see their instructor as soon as possible. Also, they should stop by the Academic Skills Center in Collis Center to register for support services.

Syllabus

Chapter 1 & 2	First Order Differential Equations
	Introduction, direction fields and classification of differential equations Introduction to matrix algera Linear and nonlinear equations; integrating factors; separable and exact equations Existence and uniqueness Theorem Euler method Autonomous equations and population dynamics
Chapter 3	Second Order Linear Equations
	Homogeneous equations Fundamental solutions, linear independence, the Wronskian Roots of the characteristic equation Nonhomogeneous equations Variation of parameters
Chapter 4	Higher Order Linear Equations
	General theory of n-th order linear equations Homogeneous equations The method of undertermined coefficients Variation of parameters
Chapter 5	Series Solutions of Second Order Linear Equations
	Review of power series, Series solutions: ordinary points Series solutions: regular singular points Bessel's equation
Chapter 7	Systems of First Order Linear Equations
	Systems of first order linear equations Review matrices and linear algebra Eigen values, eigen vectors Homogeneous linear systems Complex eigenvalues Degenerate eigenvalues
Chapter 9	Nonlinear Differential Equations and Stability
	Phase portraits of linear systems Autonomous systems and stability Almost linear systems
Chapter 10	Partial Differential Equations and Fourier Series
	Boundary value problems and Fourier Series Fourier convergence theorem, even and odd functions Separation of variables, the heat equation More heat conduction problems The wave equation Laplace's equation

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