MTH 225 DIFFERENTIAL EQUATIONS

A comprehensive final exam testing the degree of mastery of the following course objectives is required.

1. Solution of first order differential equations using the following techniques:

1.1 Separation of Variables

1.2 Homogeneous Equations

1.3 Exact

1.4 Linear

1.5. Bernoulli

2. Applications of differential equations

2.1 Linear

a. Growth and Decay
b. Cooling
c. Finance
d. Chemical Mixture
e. Orthogonal trajectories (rectangular and polar)
f. Circuits
g. Others (time permitting)

2.2 Nonlinear

a. Logistic
b. Chemical mixture
c. Vibrating mass (simple harmonic, damped and forced motion)

3. Solution of higher order linear differential equations, real coefficient

3.1 Homogeneous equation

3.2 Nonhomogeneous equation

a. Undetermined coefficients (using differential operator
b. Variation of parameters (order 2 and then order n)

4. Solution of higher order linear differential equations, variable coefficient

4.1 Equidimensional (CauchyEuler) equation

4.2 Power series solution around an ordinary point

4.3 Solutions about a regular singular point (Frobenius Case)

5. LaPlace Transform

5.1 Definition

5.2 Transforms of {1,tn, e at, sin k t, cos k t, sinh k t, cosh k t}

5.3 Inverse Transforms

5.4 Propertiestranslation, derivative of transform, transform of derivatives and of integrals, and convolution

5.5 Solution of initial value linear differential equations

5.6 Solution of a system of linear differential equationsorder two

6. Systems of Linear Differential Equations

6.1 Introduction and Basic Definitions

6.2 Operator Method for systems

6.3 Homogeneous Linear Systems

a. Real distinct eigen values
b. Repeated eigen values
c. Complex eigen values

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