
MA 235  Differential Equations4 lecture hours 0 lab hours 4 credits Course Description This course discusses the solution of firstorder differential equations, the solution of higherorder 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 firstorder differential equations by the method of separation of variables
 Determine the solution of firstorder differential equations having homogeneous coefficients
 Determine the solution of exact firstorder differential equations
 Determine appropriate integrating factors for firstorder linear differential equations
 Apply and solve firstorder differential equations of selected physical situations
 Determine the general and particular solutions of higherorder linear homogeneous differential equations with constant coefficients
 Determine the general and particular solutions of certain nonlinear secondorder homogeneous differential equations with constant coefficients using the methods of Undetermined Coefficients and Variation of Parameters
 Apply and solve secondorder 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 firstorder differential equations by separation of variables
 Solution of exact equations
 Solution of firstorder linear differential equations
 Solution of firstorder differential equations using numerical methods
 Solution of physical situations that can be modeled by firstorder differential equations
 Solution of higher order homogeneous differential equations with constant coefficients
 Solution of nonhomogeneous higherorder differential equations using the method of Undetermined Coefficients
 Solution of nonhomogeneous higherorder differential equations using the method of Variation of Parameters
 Solution of physical situations that can be modeled by higherorder 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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