Department of Physics

University of Qom

Numerical Calculations

References:

Topics:

• Numerical calculus
• Approximation of a function
• Numerical methods for matrices
• Ordinary differential equations
• Partial differential equations
• Molecular dynamics simulations(useful link)
• Monte Carlo simulations

Class Lectures (in persian):

Basis Concepts in numerical method

• Lecture-01(mp4)(pdf)

1st and 2nd order Numerical Derivatives

• Lecture-02(mp4)(pdf)
• Lecture-03(mp4)(pdf)
• Lecture-04(mp4)(pdf) (py) (HW1)

Rectangular, Trapezoidal, Simpson's 1/3 and Simpson's 3/8 Integrations

• Lecture-05(mp4)(pdf)
• Lecture-06(mp4)(pdf)

Gaussian Quadrature and 2D Integrations

• Lecture-07(mp4)(pdf)
• Lecture-08(mp4)(pdf)
• Lecture-09(mp4)(pdf) (py)(HW2)

Bisection, Newton-Raphson, Secant, False Position Finding Root Methods

• Lecture-10(mp4)(pdf)
• Lecture-11(mp4)(pdf)
• Lecture-12(mp4)(pdf) (py)

Classical Scattering

• Lecture-13(mp4)(pdf)

Solving Linear Systems: Gaussian Elimination Method, Gauss-Jordan Method, Inverse Gauss-Jordan

• Lecture-14(mp4)(pdf) (py)
• Lecture-15(mp4)(pdf) (py)
• Lecture-16(mp4)(pdf) (py)

Solving Linear Systems: LU-decomposition Method, Jacobi Iteration Method and Gauss-Seidel Iteration Method

• Lecture-17(mp4)(pdf) (py)
• Lecture-18(mp4)(pdf) (py)

Transmission of Rectangular Barriers

• Lecture-19(mp4)(pdf)

Approximation of a Function: Lagrange Interpolation, Spline Approximation, Least Square Method

• Lecture-20(mp4)(pdf)
• Lecture-21(mp4)(pdf)

Ordinary Differential Equation, 1sr order initial value Problem, Euler Method, Picard Method, Predictor-Corrector Methods, Leap-Frog Method, Rung-Kutta Methods

• Lecture-22(mp4)(pdf)
• Lecture-23(mp4)(pdf)

Ordinary Differential Equation, 2nd order initial value Problem, Driven Pendulum, Double Pendulum

• Lecture-24(mp4)(pdf)
• Lecture-25(mp4)(pdf)