MAT 352 Textbook: Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, 10th ed., Wiley

Prerequisites:  MAT 222, or MAT 221 and instructor's consent

Course Description: This course is an introduction to the concepts leading to differential equations and describes several methods used to solve general forms of these equations. Major emphasis is placed on problem solving and mathematical modelling but rigorous mathematical proofs of some of the results are presented.

Differential equations have application to problems in all scientific areas and is especially important for those in engineering related fields. This course is designed to introduce not only the mathematical vocabulary of the subject but to also instruct the student in proper methods of solving differential equations and proper ways to apply these equations to standard problems. The goal is for the student to consistently solve problems using correct technique and to additionally know how to approach similar problems in applications.

This course carries 3 hours of academic credit.
 

(From the college catalog:  This course covers the development of ordinary differential equations from special applications and concentrates on the derivation of methods for determining their solutions.  First order equations, linear equations and systems of equations and Laplace Transforms are discussed as well as further applications.)

Learning Objectives: The student will demonstrate an understanding of qualitative, analytic and numerical approaches to solving various kinds of differential equations. In particular, time permitting, the student will cover:

First-Order Equations:

• Separation of variables
• Creating and understanding direction fields
• Euler's method for single variable problems
• Classification of equilibria and the use of the phase line
• The location and effect of bifurcations
• Linear differential equations

Higher-Order Equations:

• Homogeneous Equations with Constant Coefficients
• Nonhomogeneous Equations using Undetermined Coefficients
• Nonhomogeneous Equations using Variation of Parameters

LaPlace Transforms:

• Definition and creation of formulas
• Solving second-order equations
• Impulse and Delta forcing functions

First-Order Systems:

• Predator-Prey model
• Analytic methods for finding solutions to systems
• Analyzing direction fields and the phase plane for systems
• Euler's method for autonomous systems

Linear Systems:

• Special properties
• Straight-line solutions
• Interpreting the Phase plane
• Eigenvalues and their meaning

Forcing:

• The method of undetermined coefficients
• Resonance and phasors
• Qualitative analysis for harmonic oscillators

Meetings: The format of class meetings will consist of lectures by the instructor. Student participation will be encouraged via classroom discussions as well as problem sessions where the student will present their work.

This class meets as scheduled. You are expected to be in class on time.  University policy states that a student cannot miss more than 25% of class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded according to University policy (See the Undergraduate Bulletin).

If you need special accommodations due to learning, physical, psychological, or other disabilities, please contact the Counseling and Career Development Center by phone at (601)925-3354 or by mail at P.O. Box 4013, Clinton, MS 39058.

Grading: There will be at least three exams during the semester.  Further, some projects/homework--often within the SAGE computing environment--will be assigned and graded. An average of these will count as one exam grade. Your final average will be computed by taking an average of the exam grades. The grading scale is

A=90-100

B=80-89

C=70-79

D=65-69

F=0-64

Aim now for the desired grade. Finally, all graded work will be returned to the student for keeping. If there were any question later about your grade, you would be expected to show these papers.