Subject - M.Sc. Mathematics by Dr. Rupali S. Jain

Developed By: Dr. Rupali S. Jain, Assistant Professor, School of Mathematical Sciences, SRTM University, Nanded Subject- Difference Equations, M.Sc. Mathematics, Sem-III
Sr. No.	Topics covered	Platform used and content link (Microsoft teams and OBS Studio)
1	Syllabus Introduction and preliminaries	https://youtu.be/6OibtJmO-hs
2	Real life applications in finance	https://youtu.be/Yq6lBe98MXQ
3	Real life applications in Physics	https://youtu.be/JRzeFeVcg88 https://youtu.be/Qw4LSVxHdcE
4	Airys Equation	https://youtu.be/lan6VK7t-Z0 https://youtu.be/gnDRR3eF0pU
5	Difference operator and shift operator	https://youtu.be/oA74lFikFTU
6	Properties of difference operators	https://youtu.be/jJ787ou4s4Y
7	The falling factorial power	https://youtu.be/kjDwsSZDixI
8	Summation and indefinite sums	https://youtu.be/zn5OYhKNit4
9	Properties of indefinite sums	https://youtu.be/eBxGjgw9UMg
10	Summation by parts for indefinite sums	https://youtu.be/cfGQgK3xNMo https://youtu.be/Pc5cg3IvNG0
11	Summation by parts for definite sums	https://youtu.be/hg_4ugfe0Uc https://youtu.be/bwoQmRcJlRc
12	Generating functions	https://youtu.be/VqzYH5G92e0
13	Bernoulli Polynomials and numbers	https://youtu.be/fTcIYh1oe0E
14	Euler summation formula and first order eqns	https://youtu.be/2oxGiTWUv8M
15	Solving first order difference eqns	https://youtu.be/7gZzQH197O0
16	General results for linear eqns	https://youtu.be/GKSyea1xdqs
17	Linearly dependent and independent functions	https://youtu.be/-jjQL8FWTPM
18	Casoratian of matrix	https://youtu.be/S8XTcFliVWg
19	Linear homogeneous eqns with constant coefficients	https://youtu.be/F7kHd_2yc48
20	Problems based on above topic	https://youtu.be/IJK69PNNx6s
21	Solving nonhomogeneous eqns with constant coefficeints	https://youtu.be/QBj3LH-ci6c
22	Solving system of two eqns in two unknowns	https://youtu.be/Co7zF_Kzc5U
23	Variation of parameter method	https://youtu.be/jIaHACAc0V8
24	Applications of linear homogeneous eqns	https://youtu.be/ylgrxdbz7qI
25	Difference equations with variable coefficients	https://youtu.be/NGqTchMD22M
26	Reduction order method	https://youtu.be/JHoZOp-SpGg
27	Generating function and factorial series method	https://youtu.be/c09_5KfXrSA
28	Riccati type equation	https://youtu.be/sUIar4bCqE4
29	Technique based on Lie transformation	https://youtu.be/ob5krPNKA20
30	Properties of Z- Transform	https://youtu.be/3Vv6l8fVAHw
31	Solving first orderIVPS using Z-transform	https://youtu.be/0XxQkJGVoM4
32	Solving second order IVPS	https://youtu.be/8MMn1HLUjno
33	Stability theory	https://youtu.be/GXwmB3ZdXfI
34	Solving equation u(t+1)=Au(t)	https://youtu.be/J5uPcnWz-M0
35	Examples based on Putzer algorithm	https://youtu.be/CuUJHb42xIo
36	Stability of linear systems	https://youtu.be/s5PE4bJOuVM
37	Stability of linear systems	https://youtu.be/zO1GlMeUIIo https://youtu.be/P3nj0EerOz4
38	Generalised eigen vectors	https://youtu.be/knSDFeEpRnc
39	Stable subspace theorem	https://youtu.be/Oh7EKnZD5K4
40	Phase plane analysis	https://youtu.be/1S6PeSGhq_k
41	Phase Plane Description	https://youtu.be/xUAbc8LMFqE
42	Stable and asymptotically stable fixed points	https://youtu.be/CfOvYRMGEvA https://youtu.be/qkxZIJY9za0
43	Stability of fixed points	https://youtu.be/1k8MN2J5LTw
44	Lyapunov function	https://youtu.be/jghX7PL3BS0
45	Fundamental matrices and Floquet Theory	https://youtu.be/n05YHv2fBtc
46	Floquet System	https://youtu.be/iCfRPpFuH7o
47	Discrete Floquest’s Theorem	https://youtu.be/ocJRaQijDcs