First Course on Partial Differential Equations – I
INTENDED AUDIENCE :Mathematics, Science and Engineering
PREREQUISITES : Multi variable Calculus, Linear Algebra, ordinary Differential Equations
ABOUT THE COURSE :This is intended to be a first course on the subject Partial Differential Equations, which generally requires 40 lecture hours (One semester course). So, we plan to make this course in two parts – 20 hours each. We plan to offer the first part starting in January 2021 and second part may be in July 2021 or latest by 2022.
Prof. P.S. Datti
IISc Bangalore
P.S.Datti is a former faculty at TIFR-CAM, Bangalore.
Prof. A. K. Nandakumaran
IISc Bangalore
A.K. Nandakumaran is a Professor at the Department of Mathematics, Indian Institute of Science, Bangalore.
Course layout
Week 1:Introduction, Preliminaries
Week 2:First Order Equations – Method of Characteristics
Week 3:First Order Equations ‐ multi variables and classification
Week 4:Laplace and Poisson Equations
Week 5:Laplace and Poisson Equations
Week 6:1D Heat equation
Week 7:1D wave equation
Week 8:1D wave equation
Books and references
1. A. K. Nandakumaran and P. S. Datti, Partial Differential Equations-Classical Theory with a Modern Touch, Cambridge (2020) (Cambridge-IISc Series) Expected to be in the market in April 2020.
2. L. C. Evans, Partial Differential Equations, AMS (1998)
3. Fritz John, Partial Differential Equations, Springer-Verlag, Third Edition (1978)
4. R. C. McOwen, Partial Differential Equations – Method and Applications, Pearson Education, second Edition (2005)
5. A. K. Nandakumaran, P. S. Datti and Raju K George, Ordinary Differential Equations – Principles and Applications, Cambridge (2017) (Cambridge-IISc Series), Also see, NPTEL Video course (2014) www.nptel.ac.in/courses/111108081
