24142 Differential Equation (2)

Course Description

Topics include:

The Laplace transform (the definition of Laplace transform, the inverse transform, periodic functions and the Laplace transform, the transform of the derivative, the unit-step function), Series solutions to differential equations, Fourier-Bessel Series with applications.

Learning Objective

  • A sucessful completion of this course students will be able to:
  • 1. Compute the Laplace transform of a function and inverse Laplace transform
  • 2. Use shift theorems to compute the Laplace transform and inverse Laplace transform
  • 3. Use the Laplace transform to compute solutions of differential equations
  • 4. Find the Fourier series of periodic functions
  • 5. Find the Fourier sine and cosine series for functions defined on an interval
  • 6. Half-Range Fourier Series.
  • 7. Derive the recurrence relation for the gamma function
  • 8. evaluate the gamma function for certain rational arguments
  • 9. Evaluate integrals that require the use of the gamma function in their solution
  • 10. Identify the beta function and evaluate integrals that require the use of the beta function in their solution
  • 11. Derive the relationship between the gamma function and the beta function
  • 12. Use the duplication formula to evaluate the gamma function



Books for this Course

  • 1. Differential Equations and linear algebra, Stephen W.Good, 2nd edition
  • 2. Advanced Engineering Mathematics, Erwin Kreyszing, 8th Edition

Times Offered

  • September
  • January

Course Prerequisite