Numerical Methods and Simulation Techniques

By ResearcherStore Categories: C-Science
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About Course

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 You 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...

Course Content

Numerical Methods and Simulation Techniques

  • Lec 1: Error analysis & estimates, significant digits, convergence
    00:00
  • Lec 2: Roots of Non-linear equations, Bisection method
    00:00
  • Lec 3: Newton Raphson method, Secant method
    00:00
  • Lec 4: Newton Raphson Method (Examples)
    00:00
  • Lec 5: Curve fitting and interpolation of data
    00:00
  • Lec 6: Newton’s interpolation formula, statistical interpolation of data
    00:00
  • Lec 7: Linear and Polynomial regression
    00:00
  • Lec 8:Numerical differentiation
    00:00
  • Lec 9: Numerical differentiation, Error analysis
    00:00
  • Lec 10: Numerical integration, Trapezoidal rule
    00:00
  • Lec 11: Simpson’s 1/3rd rule
    00:00
  • Lec 12: Simpson’s 1/3rd rule, Gaussian integration
    00:00
  • Lec 13: Ordinary Differential equations
    00:00
  • Lec 14: Solution of differential equation, Taylor series and Euler method
    00:00
  • Lec 15: Heun’s method
    00:00
  • Lec 16: Runge Kutta method
    00:00
  • Lec 17: Examples of differential equation: Heat conduction equation
    00:00
  • Lec 18: Introduction to Monte Carlo technique
    00:00
  • Lec 19: Details of the Monte Carlo method
    00:00
  • Lec 20: Importance sampling
    00:00
  • Lec 21: Applications: Ising model
    00:00
  • Lec 22: Introduction to Molecular Dynamics
    00:00
  • Lec 23: Verlet algorithm
    00:00
  • Lec 24: Applications of Molecular dynamics
    00:00

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