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)
Craig Sutton
Meifang Chu
Lecture Time/Room
MWF 12:30 - 1:35  Kemeny 007
MWF 10:00-11:05 Kemeny 105
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
321 Kemeny
245 Wilder

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

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 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

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.


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

return to Physics Department   /   Mathematics Department.