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Numerical Methods and Simulation Techniques for Scientists and Engineers

Numerical Methods and Simulation Techniques for Scientists and Engineers. Instructor: Prof. Saurabh Basu, Department of Physics, IIT Guwahati. 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 level. 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. (from nptel.ac.in)

Lecture 02 - Roots of Nonlinear Equations, Bisection Method


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Roots of Nonlinear Equations
Lecture 01 - Error Analysis and Estimates, Significant Digits, Convergence
Lecture 02 - Roots of Nonlinear Equations, Bisection Method
Lecture 03 - Newton-Raphson Method, Secant Method
Interpolation of Data, Curve Fitting
Lecture 04 - Newton-Raphson Method
Lecture 05 - Newton-Raphson Method (Example), Curve Fitting and Interpolation of Data
Lecture 06 - Newton's Interpolation Formula, Statistical Interpolation of Data
Numerical Differentiation
Lecture 07 - Linear and Polynomial Regression
Lecture 08 - Numerical Differentiation
Lecture 09 - Numerical Differentiation, Error Analysis
Numerical Integration
Lecture 10 - Numerical Integration, Tropizodial Rule
Lecture 11 - Simpson's 1/3rd Rule
Lecture 12 - Simpson's 1/3rd Rule, Gaussian Integration
Solution of Differential Equations
Lecture 13 - Ordinary Differential Equations
Lecture 14 - Solution of Differential Equations, Taylor Series and Euler Method
Lecture 15 - Heun's Method
Differential Equations and Monte Carlo Technique
Lecture 16 - Runge Kutta Method
Lecture 17 - Examples of Differential Equation: Heat Conduction Equation
Lecture 18 - Introduction to Monte Carlo Technique
Monte Carlo Technique and Applications
Lecture 19 - Details of Monte Carlo Method
Lecture 20 - Importance Sampling
Lecture 21 - Applications: Ising Model
Molecular Dynamics Simulation
Lecture 22 - Introduction to Molecular Dynamics
Lecture 23 - Verlet Algorithm
Lecture 24 - Applications of Molecular Dynamics