Class Lecture Notes between Minor-I and Minor-II:
| Topics | Lecture on | Source/Reference |
|---|---|---|
| The Green's Function and the Poisson Kernel on the Ball. | 30-3-2016 | Igor Yanovsky page: 204. , McOwen, pages 120-121. |
| The Green's Function and the Poisson Kernel on the Half-Space. | 28-3-2016, 29-3-2016 | Igor Yanovsky page: 198. , McOwen, pages 118-119. |
| The Green's Function and the Poisson Kernel. | 16-3-2016 | Igor Yanovsky pages: 41-43. |
| The Fundamental Solution for the Laplace Operator | 15-3-2016 | Igor Yanovsky pages: 34-36. |
| Poisson Kernels | 11-3-2016 | Igor Yanovsky: pages: 37-43. |
| 1d Heat Kernel | 9-3-2016 | Text Book: McOwen, pages 146-150, Fourier Transform and Solution of Pure Initial Problem in Chapter 5. |
| Similarity Solutions | 8-3-2016. | 1 , 2 , 3 and Text Book: McOwen, pages 156-158, Scale Invariance and Similarity Methods in Chapter 5. |
| Fundamental Solution of Heat Equation | 26-2-2016 | 1 |
| Fundamental Solution of Laplace Equation | 24-2-2016 | 1 , 2 , 3 |
| Max Principle for n dim Heat | 23-2-2016 | Text Book: McOwen, pages 144-145, Maximum Principle and Uniqueness in Chapter 5. |
| Max Principle for 1 d Heat | 17-2-2016 | 1 |
| Max Principle for Laplace equation and applications | 16-2-2016 | Text Book: McOwen, pages 107-111, Green's identities, Mean values and Max Principles in Chapter 4. |
Class Lecture Notes before Minor-I and Course Schedule:
- Lecture-14 and 15 on 9 and 10 February 2016: Exercise Problem solving sessions of Set-3
- Lecture-12 and 13 on 3 and 5 February 2016 First Order PDE: Fully Non-linear PDE, Complete Integrals and General Solutions (posted on 4 February 2016)
Source: PDE by McOwen
- Lecture-11 on 2 February 2016 First Order PDE: Fully Non-linear PDE and Method of Characteristics (posted on 1 February 2016)
Source: PDE by McOwen
- Lecture-9 and 10 on 27 and 29 January 2016 Problem Solving Sessions 1 and 2. Worked on Sheets 1 and 2 (See below attached solutions).
- No Lecture on 22 January 2016
- Lecture-7 and 8 on 19 and 20 January 2016 First Order PDE: Shock solutions of a Quasilinear PDE with discontinuous initial Data (posted on 20 January 2016)
Source: PDE by McOwen
- Lecture-6 on 15 January 2016 First Order PDE: Shock solutions of a Quasilinear PDE with continuous initial Data (posted on 20 January 2016)
Source: PDE by McOwen
- Lecture-5 on 13 January 2016 First Order PDE: Weak solutions of a Quasilinear PDE (posted on 18 January 2016)
Source: PDE by McOwen
- Lecture-4 on 12 January 2016 First Order PDE: Limitations of Methods of Characteristics and Lagrange (posted on 18 January 2016)
Source: PDE by McOwen
- Lecture-3 on 8 January 2016 First Order PDE: General solution of a Quasilinear PDE (posted on 6 January 2016)
Source: PDE by McOwen
- Lecture-2 on 6 January 2016 First Order PDE: Quasilinear case (posted on 16 November 2015)
Source: PDE by McOwen
- Lecture-1 on 5 January 2016 First Order PDE: Semilinear case (posted on 16 November 2015)
Source: PDE by McOwen
- Course Information Scheduled Lecture Dates Syllabus
Class Attendance (Updated for January and February 2016):
- Attendance-January 2016 Attendance-till-10 February 2016
- Total Lecture classes till Minor-1 are 16 (5, 6, 8, 12, 13, 15, 19, 20, 22, 27, 29 January, 2, 3, 5, 9, 10 February 2016)
- Attendance-till-26 February 2016 Attendance-till-30 March 2016
- Total Lecture classes between Minor-1 and Minor-2 are 11 (16, 17, 23, 24, 26 February, 8, 9, 11, 15, 16, 18 March)
- Total Lecture classes after Minor-2 would be 15 (28, 29, 30 March, 1, 5, 6, 8, 12, 13, 19, 22, 26, 27, 29 April, 3 May 2016)
Problem Solving Sessions between Minor-I and Minor-II
| Exercise Problem Sheets | Date of Distribution | Answers |
|---|---|---|
| Exercises-Set-4 | 15-2-2016 | 1 , solution in polar , 2 , 3 , 4, 5 |
| Exercises-Set-5 | 15-2-2016 | 1, 2, 3, 4, 5, 6, 7 |
Problem Solving Sessions before Minor-I
| Exercise Problem Sheets | Date of Distribution | Answers |
|---|---|---|
| Exercises-Set-1 | 26-1-2016 | 1, 2, 3, 4,5,6, 7, 8, 9 |
| Exercises-Set-2 | 28-1-2016 | 1, 2, 3, 4, 5 |
| Exercises-Set-3 | 5-2-2016 | 1, 2, 3, 4, 5, 6, 7, 8 |
Lecture Notes
| Topic | Source/Author |
|---|---|
| Conservation Laws | Prof. Gowda, TIFR-CAM |
| Theory and Compuations of 1st Order PDEs | Prof. Siddhartha Mishra |
| Quasilinear 1st Order PDEs | Internet |
| Mean Value Property and Max Principle for Laplacian | Internet/ Dr. Sivaji, IIT Bombay. |
| Mean Value Property and Max Principle for Laplacian | Internet/ John K. Hunter, UC-Davis. |
Textbook for Partial Differential Equations
Robert C. McOwen Partial Differential Equations, Theory and Methods,, Prentice Hall, New Jersey 2003.
Reference Books:
Partial Differential Equations, American Mathematical Society 2000, by Lawrence Evans
Partial Differential Equations in Action, Springer 2009, by Sandro Salsa
Textbooks for Ordinary Differential Equations
Reference Books:
Advanced Engineering Mathematics, by Kreyszig
Evaluation
| Minor I (11-14 February 2016) | 25% |
| Minor II (19-23 March 2016) | 25% |
| Major (5-10 May 2016) | 50% |
Minors and Major Exams
- Question Paper of Minor-1, 13 February 2016
- Answers of Minor-1, 13 February 2016
- Attendance of Minor-1
- MTL102-Minor-1 Marks
- MAL335-Minor-1 Marks
- Question Paper of Minor-2 held on 1 April
- Attendance of Minor-2
- Answers of Minor-2: Q1
- Answers of Minor-2: Q2
- Answers of Minor-2: Q3
- Answers of Minor-2: Q4
- MTL102-Minor-2 Marks
- MAL335-Minor-2 Marks
V. V. K. Srinivas Kumar