# 24142 Differential Equation (2)

## 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

3

## Books for this Course

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

• September
• January

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