Apr 22, 2018  
2017-2018 Undergraduate Academic Catalog 
    
2017-2018 Undergraduate Academic Catalog
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MA 235 - Differential Equations

4 lecture hours 0 lab hours 4 credits
Course Description
This course discusses the solution of first-order differential equations, the solution of higher-order differential equations with constant coefficients, applications of differential equations, and an introduction to the method of Laplace transforms applied to the solution of certain differential equations. (prereq: MA 231 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Determine the solution of first-order differential equations by the method of separation of variables
  • Determine the solution of first-order differential equations having homogeneous coefficients
  • Determine the solution of exact first-order differential equations
  • Determine appropriate integrating factors for first-order linear differential equations
  • Apply and solve first-order differential equations of selected physical situations
  • Determine the general and particular solutions of higher-order linear homogeneous differential equations with constant coefficients
  • Determine the general and particular solutions of certain nonlinear second-order homogeneous differential equations with constant coefficients using the methods of Undetermined Coefficients and Variation of Parameters
  • Apply and solve second-order differential equations of selected physical situations
  • Determine the Laplace transform of selected elementary functions (such as polynomials and exponential and trigonometric functions having linear arguments)
  • Determine a function having a given Laplace transform. That is, determine the inverse Laplace transform of a function
  • Solve linear differential equation of various orders using the method of Laplace transforms

Prerequisites by Topic
  • Determinants
  • Solution of algebraic equations
  • Limits including L’Hopital’s Rule
  • Differentiation of algebraic and transcendental functions
  • Integration (especially improper and the method of partial fractions)
  • Factoring of polynomials

Course Topics
  • Basic concepts
  • Solution of first-order differential equations by separation of variables
  • Solution of exact equations
  • Solution of first-order linear differential equations
  • Solution of first-order differential equations using numerical methods
  • Solution of physical situations that can be modeled by first-order differential equations
  • Solution of higher order homogeneous differential equations with constant coefficients
  • Solution of non-homogeneous higher-order differential equations using the method of Undetermined Coefficients
  • Solution of non-homogeneous higher-order differential equations using the method of Variation of Parameters
  • Solution of physical situations that can be modeled by higher-order differential equations
  • Introduction of Laplace transforms
  • Laplace transforms of elementary functions
  • Inverse Laplace transforms
  • Solution of linear differential equations with constant coefficients using Laplace transforms
  • Applications of Laplace transforms

Coordinator
Chunping Xie



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