TEW - Linear Algebra, Partial Differential Equations and Fourier Analysis (2026)

Speakers and Syllabus

Speaker	Affiliation	Topic(s)	Number of lecture hours	Number of tutorial hours
Dr. K. N. Raghavan	KREA University, Andhra Pradesh	Linear Algebra	9	2(conduct) + 2(assist)
Dr. Thirupathi Gudi	IISc, Bangalore	Partial Differential Equations	9	2(conduct) +2(assist)
Dr. G. P. Youvaraj	RIASM, Chennai	Fourier Analysis	9	2(conduct) + 2(assist)

Linear Algebra (LA):
Systems of Linear Inequalities: Standard Forms; Fourier-Motzkin Elimination
Existence of Solutions: Farkas’Lemma, Theorems of the Alternative; Convex Cones and Structure of Solutions.
Linear Programming: Existence of Optimal Solutions; Duality.

Partial Differential Equations (PDE):
Introduction to PDE, solving linear, semi-linear, quasilinear, and fully non-linear first-order equations by the method of characteristics. Conservation laws, Laplace equation (Fundamentalsolution,MeanValueProperties,MaximumprinciplesandAnalyticity). Heat equation (Fundamental Solution, infinite speed of Propagation and Maximum Principles).Wave equation (D'Alembert's solution, finite speed of propagation, method of reflection). Solutions of heat and wave equations using Transform techniques.

Fourier Analysis (FA):
Fourier series and convergence, pointwise and uniformconvergence, Gibbs phenomenon, Fourie integrals, Fourier transform and its basic properties, Plancherel and Parseval identities, Fourier series with respect to complete orthonormal sets in Hilbert spaces, Laplace transformation and its applications. 

References:

1. Kazuo Murota, Masaaki Sugihara, Linear Algebra II, Advanced Topics for Applications, (World Scientific Low-Priced Edition).

2. Gilbert Strang, Linear Algebra and Its Applications, Cengage.

3. Hoffman and Kunze, Linear Algebra, Pearson.

4. AnIntroductiontoPartialDifferentialEquations- Y.Pinchover,J. Ruben stein (Cambridge, 2005).

5. Lawrence C.Evans, Partial Differential Equations, AMS.

6. FritzJohn, Partial Differential Equations, Springer.

7. G. B. Folland, Fourier Analysis and Its Applications, BrooksandCole.

8. Elias M. Stein and Rami Shakarchi, Fourier Analysis: An Introduction, Princeton University Press.

9. T. W. Körner, Fourier Analysis, Cambridge University Press.

10. Rajendra Bhatia, Fourier Series,The Mathematical Association of America.

Time Table

Time	09.30 to 11.00 Lecture		11.15 to 12.45 Lecture		14.00 to 15.30 Lecture		15.45 to 16.45 Tutorial
Mon June 08	KNR		TG	L	GPY		TG & KNR	S
Tue June 09	GPY	T	KNR	U	TG	T	KNR & GPY	N
Wed June 10	TG	E	GPY	N	KNR	E	GPY & TG	A
Thu June 11	GPY	A	TG	C	KNR	A	TG & KNR	C
Fri June 12	TG		KNR	H	GPY		KNR & GPY	K
Sat June 13	KNR		GPY		TG		GPY & TG	S