MATH 3301 – Ordinary Differential Equations 

Spring 2006 Semester

(Required)

Catalog Data 2006-2008:        

MATH 3301: 

First order equations:  modeling and population dynamics, stability, existence and uniqueness theorem for nonlinear equations, Euler’s method.  Second order equations:  nonlinear equations via reductions methods, variation of parameters, forced mechanical vibrations, resonance and beat.  Laplace Transform:  general forcing fuctions, the convolution integral.  Systems of ODE’s:  eigenvalues and phase plane analysis.

Prerequisite:  Grade of C or better in MATH 2414..

Textbook:                                 Elementary Differential Equations, Boyes & DiPrima, 8^th ed.  

Coordinator:                             Dr. Paul Dawkins

Course Objective:                     Learn  1^st and 2^nd order differential equation solution techniques,

                                                Laplace Transforms and systems of differential equations.

Prerequisites by Topic:              “C” or better in Math 2414

Topics:

       1.     Basic Models/Direction Fields           

       2.     Classification of Differential Equations           

       3.     Linear Equation

       4.     Separable Equations

       5.     Linear & Nonlinear Equations

       6.     Modeling w/Linear Equations            

       7.     Pop. Dynamics/ Equlibrium Point

       8.     Euler’s Method

       9.     Homogeneous Equations

     10.     Complex Roots

     11.     Repeated Roots; Reduction

     12.     Linear Homogenours Equations

     13.     Lin. Independence & Wronskian

     14.     Undetermined Coefficients

     15.     Variations of Parameters

     16.     Mech. & Electrical Vibrations

     17.     Forced Mech. Vibrations

     18.     Def. Laplace Transform

     19.     Step Functions

     20.     Initial Value Problems

     21.     Dif. Equations w/Forcing Functions

     22.     Impulse Functions

     23.     The Convolution Integral

     24.     Systems of Differential Equations

     25.     Eigenvalues and Eigenvectors

     26.     Basic Theory of Systems

     27.     Homogeneous Linear Systems/Phase

     28.     Complex Eigenvalues/Phase Plane

     29.     Repeated Eigenvalues/Phase Plane

Schedule:      Three 50-minute or 75-minute lectures per week.  Varies by instructor - three or four

50-minute exams on average and a 2-hour final.