Syllabus
Unit 1
Introduction to Mathematical Modelling, linear systems of equations, eigenvalues and eigenvectors, stability of systems using eigenvalue analysis, Taylor series, numerical differentiation, numerical integration, and higher-order accuracy schemes for integration and differentiation.
Unit 2
Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), iterative methods, numerical methods including error analysis, stability and convergence, and Runge–Kutta methods.
Unit 3
Data-driven modelling, Dynamic Mode Decomposition (DMD), Koopman Theory, system identification techniques for nonlinear systems, and Physics-Informed Neural Networks.
Objectives and Outcomes
Course Objectives
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This course helps students understand established conventional computational techniques.
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This course helps students understand the concepts related to probability, statistics, linear algebra and partial differential equations, as well as the methods used to solve these equations.
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This course aims to help students implement computational methods using MATLAB and Python.
Course Outcomes
After completing this course, the students will be able to,
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CO1: Develop mathematical models to describe natural/engineering/physical systems.
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CO2: Solve differential equations using numerical schemes.
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CO3: Analyze the stability of systems using dynamical systems theory.
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CO4: Develop data-driven models of different engineering/natural/physical systems.
CO-PO Mapping
|
PO/PSO
|
PO1
|
PO2
|
PO3
|
PO4
|
PO5
|
PO6
|
PSO1
|
PSO2
|
PSO3
|
|
CO
|
|
CO1
|
3
|
3
|
2
|
2
|
–
|
–
|
3
|
1
|
2
|
|
CO2
|
3
|
3
|
3
|
2
|
–
|
–
|
3
|
1
|
2
|
|
CO3
|
3
|
3
|
2
|
3
|
1
|
–
|
3
|
2
|
2
|
|
CO4
|
2
|
3
|
3
|
3
|
1
|
1
|
3
|
3
|
3
|