### Office Hours: TTh 5-6, Skiles 224 Grader: Kunal Krishna Grader Office Hours: email him for appointment

The course will discuss the solution of Boundary Value Problems for classical Partial Differential Equations.

The text that will be used is:

David L. Powers, Boundary Value Problem 5th Edition, Harcourt Academic Press

There will be two midterm the first of which will be on Thursday September 27th.

The exercise listed are for HW collection. I will collect them every two weeks and grade 2 or 3 exercises among the one assigned.

The final greade will be based on the following rules: 50% final, 40% midterms, 10% HW. Curving will be done on the final result.

Assignments for the Long Distance students are due 1 weeks after the normal students due date.

#### Arguments Covered

• Ordinary Differential Equation (review material)
• Fourier Series and Integrals
• The Heat Equation
• The Wave Equation
• Problem in Several Dimension (time permitting)
• Numerical Methods (time permitting)

First week

Material covered:

• 0.1 (Homogeneous Linear Equations)
• 0.2 (Nonhomogeneous Linear Equations)
• 0.3 (Boundary Value Problems)
• 0.5 (Green's Function)
• 0.4 (Singular Boundary Value Problem)

Exercises:

• (0.1) 3, 11, 12, 18, 22
• (0.2) 3, 7, 12, 16
• (0.3) 3, 7, 14
• (0.4) 1, 4, 8
• (0.5) 3, 4, 8, 13

Second week

Material covered:

• 1.1 (Periodic Functions and Fourier Series)
• 1.2 (Arbitrary Period and Half Range Expansions)
• 1.3 (Convergence of Fourier Series)

Exercises:

• (1.1) 1, 6,7
• (1.2) 1, 7, 8, 9, 15
• (1.3) 2, 3

First HW collection Thursday September 6 (13 for DL student)

Third week

Material covered:

• 1.4 (Uniform convergence)
• 1.10 (Complex Methods)
• 1.5 (Operation on Fourier Series)

Exercises: (number in [] are for people with the 4th edition)

• (1.4) 1, 2, 4
• (1.10) 1 [3], 3 [5], 6 [2]
• (1.5) 6, 8, 9

Fourth week

Material covered:

• 1.6 (Mean, Error and Convergence in Mean)
• 1.8 (Numerical Determination of Fourier Coefficients)
• 1.9 (Fourier Integral)

Exercises: (number in [] are for people with the 4th edition)

• (1.6) 2, 3, 4
• (18) 3
• (1.9) 3, 5 [9], 6

Second HW collection Thursday September 20 (27 for DL student)

Fifth and Sixth week

Material covered:

• 2.1 (Derivation and Boundary Conditions)
• 2.2 (Steady States Temperatures)
• 2.3 (Example: Fixed Ends Temperatures)

Exercises:

• (2.1) 3, 5, 8
• (2.2) 1, 3, 7, 9
• (2.3) 3, 9

First Midterm will be on Thursday September 27.

See last term first miterm and solution.

Seventh week

Material covered:

• 2.4 (Example: Insulated bar)
• 2.5 (Example: Different Boundary Conditions)
• 2.6 (Example: Convection)

Exercises:

• (2.4) 1, 5, 8
• (2.5) 5 [9], 10 [6,8], 11 [3], 12 [4]
• (2.6) 3, 7, 8

Third HW collection Thursday October 11th (18 for DL student)

Eighth week

Material covered:

• 2.7 (Sturm-Liouville Problems)
• 2.8 (Expansion in Series of Eigenfunctions)
• 2.9 (Generalities on the Heat Conduction Problem)

Exercises:

• (2.7) 1, 5, 7, 8
• (2.8) 1, 2
• (2.9) 1
Nineth week

Material covered:

• 2.10 (Semi-Infinite Rod)
• 2.11 (Infinite Rod)

Exercises:

• (2.10) 2, 6
• (2.11) 1, 4, 5
Tenth week

Material covered:

• 3.1 (The Vibrating String)
• 3.2 (Solution of the Vibrating String Problem)
• 3.3 (D'Alembert Solution)

Exercises:

• (3.1) 3
• (3.2) 7 [5], 8 [6], 11 [9], 13 [11]
• (3.3) 9, 12 [10], 13 [12]

Fourth HW collection Thursday November 1st (8th for DL student)

Eleventh week

Material covered:

• 3.4 (One Dimensional Wave Equation: Generalities)
• 3.5 (Estimation of Eigenvalues)
• 3.6 (Wave Equation in Unbounded Region)

Exercises:

• (3.4)  4, 6, 8
• (3.5)  3, 6
• (3.6)  3, 6, 8

Twelfth week

Material covered:

Exercises:

• (4.1)  3, 8
• (4.2)  2, 6
• (4.3)  1, 4, 5, 9
• (4.5)  1, 2, 9

Second Midterm will be on Thursday November 15. The dead line for DL student is Monday November 25. Preparation material: last year second midterm with solution; retake for second midterm with solution; last year final.

Fifth HW collection Thursday November 29th (December 6th for DL student)