Lecture 1, January 13, 18:00-20:00 (Introduction to PDEs, Well-posedness, Transport Equation, Multi-index Notation)
Lecture 2, January 15, 16:30-18:30 (Norms and C^k Spaces, Classification of PDEs, Well-posedness, First-order PDEs, Cauchy Problem)
Lecture 3, January 20, 16:30-18:30 (Method of Characteristics, Characteristic Curves and Reduction to ODEs, Integral Surfaces and Vector Field Interpretation, Semilinear and Quasilinear First-order PDEs)
Lecture 4, January 24, 18:00-20:00 (Inviscid Burgers Equation, Shock Formation and Blow-up, Limitations of the Method of Characteristics, Lagrange’s Method for First-order PDEs, Nonlinear First-order PDEs, Existence and Uniqueness of the Cauchy Problem) & Assignment 1 (weightage 2.5 points)
Lecture 5, January 25, 18:00-20:00 (Real Analytic Functions, Power Series and Multi-index Expansions, Characterization of Analyticity via Derivative Bounds, Cauchy–Kowalevski Theorem, Analytic Existence and Uniqueness, Holmgren’s Uniqueness Theorem)
Quiz, January 29, 16:30-18:30 (weightage 10 points)
Lecture 6, February 3, 16:30-18:30 ()
Lecture 7, February 5, 16:30-18:30 ()
Lecture 8, February 10, 16:30-18:30 ()
Lecture 9, February 12, 16:30-18:30 ()
Lecture 10, February 17, 16:30-18:30 () & Assignment 2 (weightage 2.5 points)
Lecture 11, February 19, 16:30-18:30 ()
Lecture 12, February 24, 16:30-18:30 ()
Lecture 13, February 26, 16:30-18:30 ()
Midsem, March 4, 14:00-17:00 (weightage 25 points)
Lecture 14, March 10, 16:30-18:30 ()
Lecture 15, March 12, 16:30-18:30 ()
Lecture 16, March 17, 16:30-18:30 ()
Lecture 17, March 19, 16:30-18:30 () & Assignment 3 (weightage 2.5 points)
Lecture 18, March 24, 16:30-18:30 ()
Lecture 19, March 26, 16:30-18:30 ()
Lecture 20, March 31, 16:30-18:30 ()
Maundy, April 2, No Class
Lecture 21, April 7, 16:30-18:30 ()
Lecture 22, April 9, 16:30-18:30 () & Presentation (weightage 15 points)
Ambedkar Jayanti, April 14, No Class
Lecture 23, April 16, 16:30-18:30 ()
Lecture 24, April 21, 16:30-18:30 ()
Lecture 25, April 23, 16:30-18:30 () & Assignment 4 (weightage 2.5 points)
Endsem, May 6, 14:00-17:00 (weightage 40 points)