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Numerical Methods and Simulation Techniques for Scientists and Engineers

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About Course

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 You 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

Course Content

Numerical Methods and Simulation Techniques for Scientists and Engineers

  • Numerical Methods and Simulation Techniques for Scientists and Engineers [Intro Video]
    04:41
  • Lec 1: Error analysis & estimates, significant digits, convergence
    44:40
  • Lec 2: Roots of Non-linear equations, Bisection method
    44:35
  • Lec 3: Newton Raphson method, Secant method
    58:04
  • Lec 4: Newton Raphson Method (Examples)
    54:22
  • Lec 5: Curve fitting and interpolation of data
    50:28
  • Lec 6: Newton’s interpolation formula, statistical interpolation of data
    45:21
  • Lec 7: Linear and Polynomial regression
    01:00:40
  • Lec 8:Numerical differentiation
    45:20
  • Lec 9: Numerical differentiation, Error analysis
    39:08
  • Lec 10: Numerical integration, Trapezoidal rule
    50:50
  • Lec 11: Simpson’s 1/3rd rule
    56:09
  • Lec 12: Simpson’s 1/3rd rule, Gaussian integration
    49:14
  • Lec 13: Ordinary Differential equations
    01:02:30
  • Lec 14: Solution of differential equation, Taylor series and Euler method
    58:43
  • Lec 15: Heun’s method
    34:17
  • Lec 16: Runge Kutta method
    01:07:59
  • Lec 17: Examples of differential equation: Heat conduction equation
    53:18
  • Lec 18: Introduction to Monte Carlo technique
    35:48
  • Lec 19: Details of the Monte Carlo method
    50:24
  • Lec 20: Importance sampling
    51:08
  • Lec 21: Applications: Ising model
    44:22
  • Lec 22: Introduction to Molecular Dynamics
    45:46
  • Lec 23: Verlet algorithm
    58:49
  • Lec 24: Applications of Molecular dynamics
    55:05

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M
9 months ago
VERY HELPFUL COURSE
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