Available courses

Computer Lab -I

By the end of this course, students will: 
• Understand numerical computation fundamentals, error analysis, and floating- 
point arithmetic. 
• Solve equations and perform optimization using methods like Bisection, Newton
Raphson, and Gradient Descent. 
• Master numerical linear algebra, including matrix operations and eigenvalue 
computation. 
• Solve differential equations numerically with methods such as Euler and Runge
Kutta, and apply these techniques to real-world problems. 

Advanced Numerical Analysis

Course Outcome of Advanced Numerical Analysis(P)

 Students will able to

1)  Find Numerical Solution of Ordinary Differential equations: Modified Euler’s method, Predictor-corrector method, Milne’s method, Adams-Bash forth method, Boundary-value problems, Finite-difference method.

2)  Find Numerical Solution of Partial Differential equations: Finite-Difference approximations to partial derivatives, Elliptic equations, Solution of Laplace equation, Solution of Poisson’s equation,

3)   Find Solution of elliptic equations by relaxation method, parabolic equations, hyperbolic equations.

4)   Calculate Different types of approximation, least square polynomial approximation, polynomial approximation by use of orthogonal polynomials, approximation with Chebyshev polynomials.

5)   Apply Python/Scilab/Mathematica/MatLab to find Numerical Solution of Ordinary & Partial Differential equations, calculate Approximation: least square polynomial approximation, approximation with Chebyshev polynomials.

Dynamical Systems

Course Outcome of Dynamical Systems 

Students will able to

1)   Define Dynamical systems and its types as well as Iteration, Orbits, Types of Orbits, Other Orbits, The Doubling Function.                                               

2)    Do Graphical Analysis, Orbit Analysis, The Phase Portrait Analysis.

3)   Do Stability analysis of a fixed point, equilibrium point, concept of limit cycle and torus, hyperbolicity, quadratic map period doubling phenomenon.

4) Analyse Bifurcations, The Quadratic Family, Transition to Chaos, Symbolic Dynamics,    Understand Chaos. Fractals, The Julia Set, The Mandelbrot Set.            

Mathematical Modelling

Course Learning Objectives: 
1. Develop a comprehensive understanding of the definition, importance, and 
classification of mathematical modelling, and learn the process of creating elementary 
mathematical models. 
2. Learn to model single-species population dynamics using exponential and logistic 
growth models, including harvesting models and determining their critical values. 
3. Gain proficiency in modelling with ordinary differential equations, including concepts 
of stability, steady states, and applications in various fields such as economics, ecology, 
and epidemiology. 
4. Learn to construct and analyze mathematical models using difference equations, 
including applications in economics, finance, and population dynamics, and understand 
the basic theory of linear difference equations with constant coefficients. 
5. Understand the derivation and application of partial differential equations in various 
situations, including solving the one-dimensional heat equation and wave equation. 
Course Learning Outcomes: 
1. Demonstrate the ability to define, classify, and construct elementary mathematical 
models, and understand the role of mathematics in solving real-world problems. 
2. Effectively model single-species population dynamics using exponential and logistic 
growth models, analyze harvesting models, and determine critical values. 
3. Apply ordinary differential equations to model growth and decay processes, analyze 
the stability of solutions, and use these models in practical applications such as 
economics, ecology, and epidemiology, including understanding basic reproduction 
numbers. 
4. Construct and analyze mathematical models using difference equations, solve linear 
difference equations with constant coefficients, and apply these models to problems in 
economics, finance, and population dynamics. 
5. Derive and solve partial differential equations arising from various situations, 
specifically solving the one-dimensional heat equation and wave equation, and apply these solutions to practical modelling scenarios.