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
2 Real life applications in finance
3 Real life applications in Physics

4 Airys Equation

5 Difference operator and shift operator
6 Properties of difference operators
7 The falling factorial power
8 Summation and indefinite sums
9 Properties of indefinite sums
10 Summation by parts for indefinite sums

11 Summation by parts for definite sums

12 Generating functions
13 Bernoulli Polynomials and numbers
14 Euler summation formula and first order eqns
15 Solving first order difference eqns
16 General results for linear eqns
17 Linearly dependent and independent functions
18 Casoratian of matrix
19 Linear homogeneous eqns with constant coefficients
20 Problems based on above topic
21 Solving nonhomogeneous eqns with constant coefficeints
22 Solving system of two eqns in two unknowns
23 Variation of parameter method
24 Applications of linear homogeneous eqns
25 Difference equations with variable coefficients
26 Reduction order method
27 Generating function and factorial series method
28 Riccati type equation
29 Technique based on Lie transformation
30 Properties of Z- Transform
31 Solving first orderIVPS using Z-transform
32 Solving second order IVPS
33 Stability theory
34 Solving equation u(t+1)=Au(t)
35 Examples based on Putzer algorithm
36 Stability of linear systems
37 Stability of linear systems
38 Generalised eigen vectors
39 Stable subspace theorem
40 Phase plane analysis
41 Phase Plane Description
42 Stable and asymptotically stable fixed points
43 Stability of fixed points
44 Lyapunov function
45 Fundamental matrices and Floquet Theory
46 Floquet System
47 Discrete Floquest’s Theorem

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