Numerical Methods And Simulation Techniques For Scientists And Engineers

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

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

Student Ratings & Reviews

5.0

Total 1 Rating

1 Rating

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Munawaat

1 year ago

VERY HELPFUL COURSE

About Course

Numerical Methods and Simulation Techniques for Scientists and Engineers.

What Will You Learn?

Course Content

Numerical Methods and Simulation Techniques for Scientists and Engineers

Numerical Methods and Simulation Techniques for Scientists and Engineers [Intro Video]

Lec 1: Error analysis & estimates, significant digits, convergence

Lec 2: Roots of Non-linear equations, Bisection method

Lec 3: Newton Raphson method, Secant method

Lec 4: Newton Raphson Method (Examples)

Lec 5: Curve fitting and interpolation of data

Lec 6: Newton’s interpolation formula, statistical interpolation of data

Lec 7: Linear and Polynomial regression

Lec 8:Numerical differentiation

Lec 9: Numerical differentiation, Error analysis

Lec 10: Numerical integration, Trapezoidal rule

Lec 11: Simpson’s 1/3rd rule

Lec 12: Simpson’s 1/3rd rule, Gaussian integration

Lec 13: Ordinary Differential equations

Lec 14: Solution of differential equation, Taylor series and Euler method

Lec 15: Heun’s method

Lec 16: Runge Kutta method

Lec 17: Examples of differential equation: Heat conduction equation

Lec 18: Introduction to Monte Carlo technique

Lec 19: Details of the Monte Carlo method

Lec 20: Importance sampling

Lec 21: Applications: Ising model

Lec 22: Introduction to Molecular Dynamics

Lec 23: Verlet algorithm

Lec 24: Applications of Molecular dynamics

Student Ratings & Reviews