MA361 DIFFERENTIAL EQUATIONS (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 163 (Calculus II)

Course Description

First-order equations, theory of second-order linear equations, higher-order linear equations and systems, series solutions, Laplace transform and applications, and stability.

Course Content

1. Degree and Order of a Differential Equation
   • General solutions
   • Particular solutions
   • Singular solutions
2. Equations of First Order and First Degree
   • Variables
   • Separable exact equations
   • Homogeneous equations
   • Integrating factors
   • Linear equations of the
3. Equations of First Order but not of First Degree
   • Equations that can be resolved into component equations of the first degree
   • Equations solvable for y, solvable for x, homogeneous equations in x and y
   • Claraut's form
4. Linear Equations with Constant Coefficients
   • Characteristic equation with distinct and multiple roots
   • Methods for obtaining particular integrals in case when the right hand member is of the type
5. Linear Equations with Variable Coefficients
6. Integration in Series
   • Legendre's equations
   • Bessel's equations
   • Riccati's equations
7. Equations of Second Order
   • Usual methods for solving second order equations
8. Introduction to Partial Differential Equations

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