Lecture 01 - Computers and programming languages introduction

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

presentation and handouts

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

presentation and handouts

Lecture 03 - Boolean algebra, conditional statements, loops.

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

presentation and handouts

Lecture 04 - Functions and scripts

• Scripts
• Functions
• Saving and loading variables

presentation and handouts

Complimentary code

• find hypotenuse of right angle triangle hypotenuse.m
• homemade factorial script myfactorial.m
• find sin via Taylor’s series expansion mysin.m

Lecture 05 - Root finding

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

presentation and handouts

Complimentary code

• Simple bisection code bisection.m

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

presentation and handouts

Lecture 07 - Data reduction and fitting

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

presentation and handouts

Complimentary code

• Very general fitter function fitter.m
• Fitter check function fit_check.m
• Fitter function usage example fitter_usage_example.m
• Built in fit demo builtin_fitter_usage_example.m
• Built in fit check builtin_fit_check.m
• Data file for the above examples data_to_fit.dat

Lecture 08 - Data analysis example

presentation and handouts

Complimentary code

• The main analysis script day_temp_analysis_session.m. To execute it in step wise fashion use:

echodemo day_temp_analysis_session

• Outside temperature data file yearly_outside_temperatures.dat
• Helper functions
  • plot_weather_data_and_fit.m
  • reduce_with_average.m

In class practice

• Data to fit single_slit_data.dat
• Code to debug bad Ridders’ implementation

Lecture 09 - Numerical integration

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

presentation and handouts

Lecture 10 - Numerical integration continued

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

presentation and handouts

Complimentary code

• very primitive 1d integration without checks integrate_in_1d.m
• very primitive 2d integration without checks integrate_in_2d.m
• sample function for 2d integration func2d.m

In class practice: The volume of multi-dimensional sphere

Lecture 11 - Practical example: diffraction

• Practical example: diffraction

presentation and handouts

Lecture 12 - Practical example: diffraction

• Practical example: diffraction - continued

presentation and handouts

Complimentary code

• single point intensity from a mask image beam_intensity_at_point_from_image.m
• overall image created by diffracted light on a mask diffracted_image_at_target.m
• function to show source and target images show_diffraction.m
• simple demo of diffraction on a single slit demo_diffraction_on_a_single_slit.m
• simple demo of diffraction on a double slit demo_diffraction_on_a_double_slit.m
• simple demo of diffraction on a double slit demo_diffraction_on_a_disk.m
• demo of diffraction on the WM logo demo_diffraction_on_the_wm_image.m, running this demo takes 6 and half hours on my 6 core AMD computer
  • input mask mask_WM.png image for WM logo diffraction
  • resulting diffracted target image image_wm_diffracted.png

Lecture 13 - Random number generators and random processes

• Statistic and probability intro
• Random number generators

presentation and handouts

Complimentary code

• pegboard.m
• home made LCG generator lcgrand.m
• simple check script for the period of LCG check_lcgrand.m

Lecture 14 - Monte Carlo simulations

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

presentation and handouts

Complimentary code

• bet_outcome.m
• plot_gain_vs_bet_fraction.m
• doors_game.m
• doors_game_check.m
• disease_outcome.m
• colony_life.m

Lecture 15 - Optimization problem

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

presentation and handouts

Complimentary code

• calculation of black body radiation black_body_radiation.m
• a company profit vs money distribution profit.m

Lecture 16 - Multi-D optimization problem

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

presentation and handouts

Complimentary code

• Simple function which makes a 3D plot of a function of 2 variables plot3dForXY.m
• Usage example plot_sinc_3d.m of above function which plots the sample function z=-sinc(r) where r=sqrt(xx+yy) fsample_sinc.m
• Merit function for the suspended weights problem EconstrainedSuspendedWeights.m
• Merit function for the potential well problem merit_psi.m
• Complete example of the potential well problem potential_well_example.m

Lecture 17 - Combinatorial optimization

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

presentation and handouts

Complimentary code

• backpack_binary.m
• permutation.m
• traveler_comb.m
• cities_for_combinatorial_search.dat

Lecture 18 - Simulated annealing/Metropolis and genetic optimization

• Simulated annealing/Metropolis algorithm
• Genetic algorithm

presentation and handouts

Complimentary code

• backpack_metropolis.m
• backpack_check.m

Lecture 19 - Ordinary Differential equations

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

presentation and handouts

Complimentary code

• Euler’s method ODE solver odeeuler.m
• Example of the free fall numerical solution with Euler’s method ode_free_fall_example.m
  • free fall forces calculation code free_fall_forces.m
• Example of stability issues in the ODE solvers ode_unstable_example.m
  • forces calculation code ode_unstable_forces.m

Lecture 20 - Ordinary Differential equations continued

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

presentation and handouts

Complimentary code

• parachute jumper model (time dependent force) ode_parachute_jump_model.m
• projectile motion with air drag ode_projectile_with_air_drag_model.m
• predator and prey model shows oscillations ode_predator_prey_model.m
• Lorenz attractor model ode_lorenz_attractor.m

Lecture 21 - System of linear algebraic equations

• Matlab solvers

presentation and handouts

Complimentary code

• the mobile problem mobile.m
• the Wheatstone bridge problem wheatstone_bridge.m

Lecture 22 - Data interpolation

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

presentation and handouts

Complimentary code

• x,y data to interpolate data_for_interpolation1.m
• x,y parametric points for a circle data_for_interpolation2.m
• nearest neighbor interpolation interp_nearest.m
• linear interpolation interp_linear.m
• sample code comparing results of different interpolation algorithm sample_plots_for_inerpolation.m

Lecture 23 - Fourier transform

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

presentation and handouts

Complimentary code

• Fourier series for |t| fourier_abs.m
• Fourier series for step function fourier_step.m

Lecture 24 - Discrete Fourier Transform and filters

• Discrete Fourier transform
• Nyquist criteria
• DFT filters

presentation and handouts

Complimentary code

• filtersdemo.m
• fourier_frequencies.m
• freq_space_low_pass_filter.m
• voice_record.wav
• enlarge font size for plots niceplotset.m

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

presentation and handouts

Complimentary code

Voice filtering demo

• voice record with monochromatic noise voice_record_l27.wav
• voice filtering demo filter_voice_demo_l27.m
• fourier_frequencies.m
• filter application help function filter_application.m
• enlarge font size for plots niceplotset.m

Weather data analysis

• analysis demo weather_analysis_demo.m
• outside temperature data yearly_outside_temperatures.dat
• reduce_with_average.m

Lecture 26 - High performance computing

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

presentation and handouts

Complimentary code

• for loop example for_script.m
• parfor loop example parfor_script.m

Lecture 27 - Secure communications

• Secure communication and encryption.

presentation and handouts

Lecture 28 - Sorting

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

presentation and handouts

See what the president Obama (a senator at that time) has to say about the bubble sort method. Skip to the 34th second.

Complimentary code

• qsort.m

Lecture 29 - Other useful tools

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

presentation and handouts

Problem files

Data file for problems 1, 2, and 3 capsule_and_plane_problem_datafile1.mat.

For problem 1 and 2 use the following, additional to the data in the above file, input

Ve=900;
ElAng=pi/3;

Function templates

• capsule_flight_simulator.m
• capsule_launch_solution.m
• capsule_max_height_parameters.m

Voice messages for problem 4. Each group must decode only the one assigned to them.

• noisy_msg1.wav Marcus and Kevin
• noisy_msg2.wav Ryan, Anna, and Peter
• noisy_msg3.wav Jacob G., Tom F., Patrick
• noisy_msg4.wav Wenqing and Benjamin H.
• noisy_msg5.wav Benjamin K. and William
• noisy_msg6.wav Wyndham, Evan, and Jacob M.
• noisy_msg7.wav Chloe, Alexandra, and Tom S.
• noisy_msg8.wav Matthew and Gregory
• noisy_msg9.wav TBA
• noisy_msg10.wav TBA

Some test cases to help you with your simulator check

For problem 1

>> [time,x,y] = capsule_flight_simulator(300, 2, 500, .1, 2*pi/5 );
>> time(end)
ans =
   42.8555
>> x(end)
ans =
   1.6716e+03
>> y(end)
ans =
   5.0681e-04

For problem 2

>> [MaxHeight, t_at_max, vx_at_max, x_at_max] = capsule_max_height_parameters(300, 2, 500, .1, 2*pi/5 )
MaxHeight =
   2.2089e+03

t_at_max =
   16.9071

vx_at_max =
   38.2439

x_at_max =
   1.0391e+03

For problem 3 which is run against file capsule_and_plane_problem_datafile2.mat.

>> [ElevationAngle, Vescape, Tlaunch] = capsule_launch_solution( 'capsule_and_plane_problem_datafile2.mat');

Vescape =
  637.3440


ElevationAngle =
    1.4033


Tlaunch =
    7.1754