Physics 256 - Tentave list of topics

Lecture 01 - Computers and programming languages introduction

• Class goals and structure
• Computers introduction
• Programming languages overview
• Discretization - the main weakness of computers
• Binary representation

Lecture 02 - Introduction to Matlab

• Matlab as a fancy calculator
• Efficient editing
• Help related commands
• Operators precedence
• Matrices
• Colon (:) operator
• Plotting
• Array element-wise arithmetic operators

Lecture 03 - Boolean algebra, conditional statements, loops.

• Boolean algebra
• Comparison operators
• Conditional statements
• Loops
• Series

Lecture 04 - Functions and scripts

• Scripts
• Functions
• Saving and loading variables

Lecture 05 - Root finding

• Root finding problem
• Bisection method
• False position method
• Solution convergence

Lecture 06 - Root finding continued

• Secant method
• Newton-Raphson method
• Numerical derivative of a function
• Ridders method
• Root finding algorithms gotchas
• Root finding algorithms summary

Lecture 07 - Data reduction and fitting

• Goodness of the fit
• Parameter uncertainty estimations
• Homemade implementation of the fitter
• Matlab built-ins

Lecture 08 - Data analysis example

Lecture 09 - Numerical integration

• Integration problem statement
• The Rectangle method
• Trapezoidal method
• Simpson method

Lecture 10 - Numerical integration continued

• Monte Carlo Integration
• Numerical Integration methods error estimates
• Multidimensional integration
• Matlab functions for integration

Lecture 11 - Practical example: diffraction

• Practical example: diffraction

Lecture 12 - Practical example: diffraction

• Practical example: diffraction - continued

Lecture 13 - Random number generators and random processes

• Statistic and probability intro
• Random number generators

Lecture 14 - Monte Carlo simulations

• Coin flipping bets
• Anonymous function and their use
• Matlab arrayfun
• The Monty Hall Paradox
• Disease spread

Lecture 15 - Optimization problem

• Introduction to optimization
• Matlab built in 1D minimization - fminbnd
• 1D optimization - golden section search

Lecture 16 - Multi-D optimization problem

• Multi-D optimization
• Matlab built in Multi-D minimization - fminsearch
• Sample problems

Lecture 17 - Combinatorial optimization

• Introduction to the combinatorial problem
• Backpack problem - brute force approach
• Traveling salesman problem
• Permutation generating algorithm

Lecture 18 - Simulated annealing/Metropolis and genetic optimization

• Simulated annealing/Metropolis algorithm
• Genetic algorithm

Lecture 19 - Ordinary Differential equations

• ODE - ordinary differential equations
• Cauchy boundary conditions
• Euler’s method

Lecture 20 - Ordinary Differential equations continued

• The second-order Runge-Kutta method (RK2)
• The forth-order Runge-Kutta method (RK4)
• Matlab functions for ODEs

Lecture 21 - System of linear algebraic equations

• Matlab solvers

Lecture 22 - Data interpolation

• Nearest neighbor interpolation
• Linear interpolation
• Polynomial fit
• Cubic spline interpolation
• Matlab built in interpolation
• Extrapolation

Lecture 23 - Fourier transform

• Fourier series
• Discrete Fourier transform (DFT)
• Matlab implementation

Lecture 24 - Discrete Fourier Transform and filters

• Discrete Fourier transform
• Nyquist criteria
• DFT filters

Lecture 25 - Digital filters

• Speed of FFT
• Low-pass filter
• High-pass filter
• Band-pass filter
• Band-stop filter
• Brick wall filters artifacts
• Windowing
• Other DFT applications

Lecture 26 - High performance computing

• Limits to computing speed
• Parallel computing
• Matlab parallel tools

Lecture 27 - Secure communications

• Secure communication and encryption.

Lecture 28 - Sorting

• Bubble sort method
• Quick sort method
• Heap sorting method
• The vector heap representation
• Matlab built ins ‘issorted’ adn ‘sort’

Lecture 29 - Other useful tools

• Scientist toolbox
• Free software
• Version control software
• Final remarks