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Numerical Methods and Simulation Techniques

  • Course level: All Levels
  • Categories C-Science
  • Last Update 25/06/2021

Description

The course contains very important aspects of the modern-day course curriculum, namely, numerical methods and simulation techniques that are going to be of utmost importance to both undergraduate and graduate levels.

Most of the real-life problems are unsolvable using known analytic techniques thus depending on numerical methods is imperative.

The course introduces basic and key simulation techniques that are going to be useful to academia and industry alike. Even if the software packages, such as Mathematica, Matlab, etc are available for most of the numeric computations, yet one should be aware of the techniques that are inbuilt into the software.

 

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What Will I Learn?

  • -Introduction to Numerical analysis, Importance of error and their calculations
  • -Learn and Understand Root Finding Method of non-linear equations, Bisection Method, Newton Raphson Method,Secant method, Regula- Falsi method.
  • -Learn Numerical differentiation, central difference methods, higher order derivatives, errors also Numerical integration, Simpson’s 1/3 rd rule, Simpson’s 3/8 th rule, local and global error analysis
  • -Learn Eigenvalue problems, Heun’s method, Euler’s method, Runge Kutta Method, Gerschgorin disc theorem ,Jacobi method And much more...

Topics for this course

24 Lessons

Numerical Methods and Simulation Techniques

Lec 1: Error analysis & estimates, significant digits, convergence00:00:00
Lec 2: Roots of Non-linear equations, Bisection method00:00:00
Lec 3: Newton Raphson method, Secant method00:00:00
Lec 4: Newton Raphson Method (Examples)00:00:00
Lec 5: Curve fitting and interpolation of data00:00:00
Lec 6: Newton’s interpolation formula, statistical interpolation of data00:00:00
Lec 7: Linear and Polynomial regression00:00:00
Lec 8:Numerical differentiation00:00:00
Lec 9: Numerical differentiation, Error analysis00:00:00
Lec 10: Numerical integration, Trapezoidal rule00:00:00
Lec 11: Simpson’s 1/3rd rule00:00:00
Lec 12: Simpson’s 1/3rd rule, Gaussian integration00:00:00
Lec 13: Ordinary Differential equations00:00:00
Lec 14: Solution of differential equation, Taylor series and Euler method00:00:00
Lec 15: Heun’s method00:00:00
Lec 16: Runge Kutta method00:00:00
Lec 17: Examples of differential equation: Heat conduction equation00:00:00
Lec 18: Introduction to Monte Carlo technique00:00:00
Lec 19: Details of the Monte Carlo method00:00:00
Lec 20: Importance sampling00:00:00
Lec 21: Applications: Ising model00:00:00
Lec 22: Introduction to Molecular Dynamics00:00:00
Lec 23: Verlet algorithm00:00:00
Lec 24: Applications of Molecular dynamics00:00:00
33 £

Enrolment validity: Lifetime