Jul 05, 2022  
2020-2021 Undergraduate Academic Catalog 
2020-2021 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 382 - Laplace and Fourier Transforms

3 lecture hours 0 lab hours 3 credits
Course Description
This course introduces the theoretical concepts and uses of the Laplace and Fourier transforms. It includes Laplace transform of special functions, properties, operations and using Laplace transforms to solve ordinary and partial differential equations. It also includes Fourier series, Fourier Integral representation and Fourier transform of special functions, properties, operations and using them in partial differential equations. (prereq: MA 232  or MA 2323 , and MA 235 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Find Laplace and inverse Laplace transforms using a table
  • Find Fourier transforms
  • Solve linear differential equations and systems of equations with input functions, such as: continuous, piecewise continuous, unit step, impulse and periodic
  • Solve certain types integral, and integro-differential equations
  • Solve certain classes of linear partial differential equations

Prerequisites by Topic
  • Improper integrals
  • Infinite series
  • Linear differential equations

Course Topics
  • Basic properties of Laplace transforms and transforms of special functions
  • Transforms of derivatives and integrals and derivatives of transform
  • Application to differential equations
  • The unit step function
  • The Dirac delta function
  • Applications of step and impulse functions
  • Periodic functions and their applications
  • Convolution and applications
  • Solving integral equations
  • Fourier series
  • Fourier integral representation
  • Fourier transforms and its properties
  • Fourier sine and cosine transforms
  • Application of Fourier transforms to partial differential equation

Dr. Yvonne Yaz

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