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Differential Equations
MAT 352 Textbook: Differential Equations, 2nd edition, by Blanchard, Devaney and Hall
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
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
LaPlace Transforms:
Definition and creation of formulas
Solving second-order equations
Impulse and Delta forcing functions
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; HYPERLINK "http://www.mc.edu/publications/policies/academic/219.html" http://www.mc.edu/publications/policies/academic/219.html).
MISSISSIPPI COLLEGE ACADEMIC POLICIES:
Students should consult the Mississippi College policy manual located at http://www.mc.edu/resources/publications/policies/ for official information regarding:
Class attendance - Policy 2.10
Grading - Policy 2.15
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Counseling and Career Services - Policy 2.25
Research - Policy 2.27
Counseling and Testing Center - Policy 2.34
Students who may require accomodation due to a documented handicap should follow the procedures located at http://www.mc.edu/about/offices/counseling/disabilities/
The Generic Grading Scale for this course is A = 90-100, B = 80-89, C = 70-79, D = 60-69. Individual instructors are free to choose a different grading scheme so students should consult their section's particular syllabus for the official grading scale to be utilized.
Tutoring Hours:
Hours and location for the departmental tutoring center are posted at http://www.mc.edu/academics/academic-tutoring/ .
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