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