Developed By: Dr. Rupali S. Jain, Assistant Professor, School of Mathematical Sciences, SRTM University, Nanded Subject- Difference Equations, M.Sc. Mathematics, Sem-III |
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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 | |
4 | Airys Equation | |
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 | |
11 | Summation by parts for definite sums | |
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 |
Subject - M.Sc. Mathematics by Dr. Rupali S. Jain
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