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Numerical Methods and Simulation Techniques for Scientists and Engineers

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

Description

Numerical Methods and Simulation Techniques for Scientists and Engineers.

The course contains very important aspects of the modern-day course curriculum, namely, numerical method 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 numerical methods and the 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.

INTENDED AUDIENCE: Students, Lecturers from Engineering colleges and Universities. Also, Industry people may be interested who do simulation

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What Will I Learn?

  • Week 1: Introduction to Numerical analysis, Importance of error and their calculations, Examples
  • Week 2: Root Finding Method of non-linear equations, Bisection Method, Newton Raphson Method,
  • Secant method, Regula- Falsi method, Practical examples.
  • Week 3: Curve fitting method, linear and non-linear fitting, Linear interpolation, Lagrange interpolation the method, Newton Interpolation formula, Practical examples.
  • Week 4: Numerical differentiation, central difference methods, higher-order derivatives, errors, practical examples.
  • Week 5: Numerical integration, Simpson’s 1/3 rd rule, Simpson’s 3/8 th rule, local and global error analysis
  • , practical examples.
  • Week 6: Eigenvalue problems, Heun’s method, Euler’s method, Runge Kutta Method, Gerschgorin disc theorem, Jacobi method, Practical examples
  • Week 7: Simulation Techniques, Random numbers, Monte Carlo Method, Importance Sampling, Metropolis Algorithm, Heat- bath algorithm, practical Examples
  • Week 8: Molecular dynamics, interaction and forces in molecular systems, MD and Verlet algorithm, correlations, practical examples

Topics for this course

25 Lessons

Numerical Methods and Simulation Techniques for Scientists and Engineers

Numerical Methods and Simulation Techniques for Scientists and Engineers [Intro Video]4:41
Lec 1: Error analysis & estimates, significant digits, convergence44:40
Lec 2: Roots of Non-linear equations, Bisection method44:35
Lec 3: Newton Raphson method, Secant method58:04
Lec 4: Newton Raphson Method (Examples)54:22
Lec 5: Curve fitting and interpolation of data50:28
Lec 6: Newton’s interpolation formula, statistical interpolation of data45:21
Lec 7: Linear and Polynomial regression1:00:40
Lec 8:Numerical differentiation45:20
Lec 9: Numerical differentiation, Error analysis39:08
Lec 10: Numerical integration, Trapezoidal rule50:50
Lec 11: Simpson’s 1/3rd rule56:09
Lec 12: Simpson’s 1/3rd rule, Gaussian integration49:14
Lec 13: Ordinary Differential equations1:02:30
Lec 14: Solution of differential equation, Taylor series and Euler method58:43
Lec 15: Heun’s method34:17
Lec 16: Runge Kutta method1:07:59
Lec 17: Examples of differential equation: Heat conduction equation53:18
Lec 18: Introduction to Monte Carlo technique35:48
Lec 19: Details of the Monte Carlo method50:24
Lec 20: Importance sampling51:08
Lec 21: Applications: Ising model44:22
Lec 22: Introduction to Molecular Dynamics45:46
Lec 23: Verlet algorithm58:49
Lec 24: Applications of Molecular dynamics55:05

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VERY HELPFUL COURSE

Numerical Methods
Free

Enrolment validity: Lifetime

Requirements

  • Basic level Mathematics course