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Sep 08, 2024
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MA 3502 - Engineering Mathematics II4 lecture hours 0 lab hours 4 credits Course Description Solution of first order equations, higher order linear equations and initial value problems, the methods of undetermined coefficients, variation of parameters, and Laplace transforms. (prereq: MA 225, MA 231 /MA 2314 or equivalent) Course Learning Outcomes Upon successful completion of this course, the student will be able to:
- Determine the solution of a first order differential equations by the method of separation of variables
- Solve exact equations
- Determine appropriate integrating factors for first order linear equations
- Determine the general solution of higher order linear homogeneous equations with constant coefficients
- Determine the general and particular solutions of certain linear non-homogenous equations using the methods of undetermined coefficients and variation of parameters
- Determine the Laplace transform and inverse Laplace transform of certain elementary functions
- Solve certain linear differential equations using Laplace transforms
Prerequisites by Topic
- Differentiation of elementary functions for all topics
- Integration techniques for solving differential separable and exact equations and for variation of parameters
- Improper integrals for Laplace transforms
Course Topics
- Basic concepts of differential equations
- Solution of first order equations by separation of variables
- Solution of exact equations
- Solution of first order linear non-homogeneous equations
- Solution of higher order linear homogeneous differential equations with constant coefficients
- Solution of higher order linear non-homogeneous differential equations using the method of undetermined coefficients
- Solution of higher order linear non-homogeneous differential equations using the method of variation of parameters
- Introduction to Laplace transforms
- Laplace transforms of elementary functions
- Inverse Laplace transforms
- Operational properties: Laplace transforms and inverse Laplace transforms involving transforms of derivatives, derivatives of transforms, exponential shift (translation on the s-axis) and Heaviside function (translation on the t-axis), Dirac delta function and periodic functions
- Solution of linear differential equations using Laplace transforms
Coordinator Dr. Anthony van Groningen
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