LECTURE NOTES

1. Derivation of the Heat Equation
2. Derivation of the Wave Equation
3. Laplace Equation
4. Principle of Superposition
5. Method of Separation of Variables
6. Fourier Series Part 1: Definition and examples
   
7. Fourier Series Part 2: Convergence
8. Fourier Series Part 3: Applications
9. Sturm-Liouville Problems: Generalized Fourier Series
10. Non Homogeneous BVP and Higher Dimensions
11. Bessel Equations and Bessel Functions
12. Fourier-Bessel Series and BVP in Cylindrical Coordinates
13. Legendre Polynomials and Applications

Solutions to odd problems:

1. Solutions-Note1
2. Solutions-Note2
3. Solutions-Note3
4. Solutions-Note4
5. Solutions-Note5
6. Solutions-Note6
7. Solutions-Note7
8. Solutions-Note8
9. Solutions-Note9
10. Solutions-Note10
11. Solutions-Note11
12. Solutions-Note12
13. Solutions-Note13

Assignments:

• HW1
• HW1-Solutions
• TEST 2 Solutions
• HW3
• TEST 3 Solutions