V. V. K. Srinivas Kumar

Dept. of Mathematics


MTL102: Differential Equations

II semester: 2015-16

V. V. K. Srinivas Kumar


Lecture Timings: Tue, Wed and Fri 10:00AM to 10:50AM
Lecture Room: LH111

Lecture Topics AFTER Minor-II:

Topics Lecture on Source/Reference
Liaponov functions and Applications 29-4-2016, 3-5-2016 Text Book: G F Simmons and Advanced Engineering Mathematics by Kreyszig
Linear and Nonlinear Stability Analysis 26-4-2016, 27-4-2016 Text Book: G F Simmons and Advanced Engineering Mathematics by Kreyszig
Phase plane analysis 19-4-2016, 22-4-2016 Text Book: G F Simmons and Advanced Engineering Mathematics by Kreyszig
Comparison Theorems of Sturm and Sturm Liouville Eigen value Problems 12-4-2016 and 13-4-2016Text Book: Differential Equations by G.F Simmons.
Continuous Dependence of Solutions, Nonlocal Existence of solutions 8-4-2016 Text Book: Coddington, pages 252-262
Picard's Theorem: Existence and Uniqueness (Local) 6-4-2016Text Book: Coddington, pages 250-252.
Lipschitz Condition (THE VECTOR CASE) 5-4-2016Text Book: Coddington-Pages 247-249
Existence and Uniqueness of solutions to System of Semilinear and Nonlinear ODEs (THE VECTOR CASE) 5-4-2016Text Book: Chapter 6 of Earl A Coddington: An introduction to Ordinary Differential Equations, pages 229-261.
Continuation of Chapter-5: Method of Successive Approximations (THE SCALAR CASE) ---Text Book: Coddington, pages 208-227, Chapter 5, Solutions of first order equations.
General first order ODEs-Method of Successive Approximations (THE SCALAR CASE) ----Text Book: Coddington, pages 200-205, Chapter 5, Solutions of first order equations.


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 23-2-2016Text 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 16-2-2016Text 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-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

Class Attendance (Updated for January and February 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

  • An introduction to Ordinary Differential Equations by Coddington,
  • Differential Equations Theory, Technique and Practice by G.F. Simmons and Stevan G. Krantz,
  • 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

    V. V. K. Srinivas Kumar