24142 Differential Equation (2)
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.
- 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
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