Programming with MatLab for Scientists. A Beginner’s Introduction

Half Title
Title Page
Copyright Page
Contents
Preface
Part I: Computing Essentials
	1: Computers and Programming Languages:An Introduction
		1.1 Early History of Computing
		1.2 Modern Computers
			1.2.1 Common features of a modern computer
		1.3 What Is Programming?
		1.4 Programming Languages Overview
		1.5 Numbers Representation in Computers and Its Potential Problems
			1.5.1 Discretization—the main weakness of computers
			1.5.2 Binary representation
			1.5.3 Floating-point number representation
			1.5.4 Conclusion
		1.6  Self-Study
	2: MATLAB Basics
		2.1 MATLAB's Graphical User Interface
		2.2 MATLAB as a Powerful Calculator
			2.2.1 MATLAB's variable types
			2.2.2 Some built-in functions and operators
				2.2.2.1 Assignment operator
			2.2.3 Operator precedence
			2.2.4 Comments
		2.3 Efficient Editing
		2.4 Using Documentation
		2.5 Matrices
			2.5.1 Creating and accessing matrix elements
			2.5.2 Native matrix operations
				2.5.2.1 Matrix element-wise arithmetic operators
			2.5.3 Strings as matrices
		2.6 Colon (:) Operator
			2.6.1 Slicing matrices
		2.7 Plotting
			2.7.1 Saving plots to files
		2.8  Self-Study
	3: Boolean Algebra, Conditional Statements, Loops
		3.1 Boolean Algebra
			3.1.1 Boolean operators precedence in MATLAB
			3.1.2 MATLAB Boolean logic examples
		3.2 Comparison Operators
			3.2.1 Comparison with vectors
			3.2.2 Comparison with matrices
		3.3 Conditional Statements
			3.3.1 The if-else-end statement
			3.3.2 Short form of the ``if'' statement
		3.4 Common Mistake with the Equality Statement
		3.5 Loops
			3.5.1 The ``while'' loop
			3.5.2 Special commands ``break'' and ``continue''
			3.5.3 The ``for'' loop
				3.5.3.1 Series implementation example
		3.6  Self-Study
	4: Functions, Scripts, and Good Programming Practice
		4.1 Motivational Examples
			4.1.1 Bank interest rate problem
			4.1.2 Time of flight problem
		4.2 Scripts
			4.2.1 Quadratic equation solver script
		4.3 Functions
			4.3.1 Quadratic equation solver function
		4.4 Good Programming Practice
			4.4.1 Simplify the code
			4.4.2 Try to foresee unexpected behavior
			4.4.3 Run test cases
			4.4.4 Check and sanitize input arguments
			4.4.5 Is the solution realistic?
			4.4.6 Summary of good programming practice
		4.5 Recursive and Anonymous Functions
			4.5.1 Recursive functions
			4.5.2 Anonymous functions
		4.6  Self-Study
Part II: Solving Everyday Problems with MATLAB
	5: Solving Systems of Linear AlgebraicEquations
		5.1 The Mobile Problem
		5.2 Built-In MATLAB Solvers
			5.2.1 The inverse matrix method
			5.2.2 Solution without inverse matrix calculation
			5.2.3 Which method to use
		5.3 Solution of the Mobile Problem with MATLAB
			5.3.1 Solution check
		5.4 Example: Wheatstone Bridge Problem
		5.5 Self-Study
	6: Fitting and Data Reduction
		6.1 Necessity for Data Reduction and Fitting
		6.2 Formal Definition for Fitting
			6.2.1 Goodness of the fit
		6.3 Fitting Example
		6.4 Parameter Uncertainty Estimations
		6.5 Evaluation of the Resulting Fit
		6.6 How to Find the Optimal Fit
			6.6.1 Example: Light diffraction on a single slit
			6.6.2 Plotting the data
			6.6.3 Choosing the fit model
			6.6.4 Making an initial guess for the fit parameters
			6.6.5 Plotting data and the model based on the initial guess
			6.6.6 Fitting the data
			6.6.7 Evaluating uncertainties for the fit parameters
		6.7 Self-Study
	7: Numerical Derivatives
		7.1 Estimate of the Derivative via the Forward Difference
		7.2 Algorithmic Error Estimate for Numerical Derivative
		7.3 Estimate of the Derivative via the Central Difference
		7.4  Self-Study
	8: Root Finding Algorithms
		8.1 Root Finding Problem
		8.2 Trial and Error Method
		8.3 Bisection Method
			8.3.1 Bisection use example and test case
				8.3.1.1 Test the bisection algorithm
				8.3.1.2 One more example
			8.3.2 Possible improvement of the bisection code
		8.4 Algorithm Convergence
		8.5 False Position (Regula Falsi) Method
		8.6 Secant Method
		8.7 Newton–Raphson Method
			8.7.1 Using Newton–Raphson algorithm with the analytical derivative
			8.7.2 Using Newton–Raphson algorithm with the numerical derivative
		8.8 Ridders' Method
		8.9 Root Finding Algorithms Gotchas
		8.10 Root Finding Algorithms Summary
		8.11 MATLAB's Root Finding Built-in Command
		8.12  Self-Study
	9: Numerical Integration Methods
		9.1 Integration Problem Statement
		9.2 The Rectangle Method
			9.2.1 Rectangle method algorithmic error
		9.3 Trapezoidal Method
			9.3.1 Trapezoidal method algorithmic error
		9.4 Simpson's Method
			9.4.1 Simpson's method algorithmic error
		9.5 Generalized Formula for Integration
		9.6 Monte Carlo Integration
			9.6.1 Toy example: finding the area of a pond
			9.6.2 Naive Monte Carlo integration
			9.6.3 Monte Carlo integration derived
			9.6.4 The Monte Carlo method algorithmic error
		9.7 Multidimensional Integration
			9.7.1 Minimal example for integration in two dimensions
		9.8 Multidimensional Integration with Monte Carlo
			9.8.1 Monte Carlo method demonstration
		9.9 Numerical Integration Gotchas
			9.9.1 Using a very large number of points
			9.9.2 Using too few points
		9.10 MATLAB Functions for Integration
		9.11  Self-Study
	10: Data Interpolation
		10.1 The Nearest Neighbor Interpolation
		10.2 Linear Interpolation
		10.3 Polynomial Interpolation
		10.4 Criteria for a Good Interpolation Routine
		10.5 Cubic Spline Interpolation
		10.6 MATLAB Built-In Interpolation Methods
		10.7 Extrapolation
		10.8 Unconventional Use of Interpolation
			10.8.1 Finding the location of the data crossing y=0
		10.9 Self-Study
Part III: Going Deeper and Expanding the Scientist's Toolbox
	11: Random Number Generators and Random Processes
		11.1 Statistics and Probability Introduction
			11.1.1 Discrete event probability
			11.1.2 Probability density function
		11.2 Uniform Random Distribution
		11.3 Random Number Generators and Computers
			11.3.1 Linear congruential generator
			11.3.2 Random number generator period
		11.4 How to Check a Random Generator
			11.4.1 Simple RNG test with Monte Carlo integration
		11.5 MATLAB's Built-In RNGs
		11.6 Self-Study
	12: Monte Carlo Simulations
		12.1 Peg Board
		12.2 Coin Flipping Game
		12.3 One-Dimensional Infection Spread
		12.4 Self-Study
	13: The Optimization Problem
		13.1 Introduction to Optimization
		13.2 One-Dimensional Optimization
			13.2.1 The golden section optimum search algorithm
				13.2.1.1 Derivation of the R coefficient
			13.2.2 MATLAB's built-in function for the one-dimension optimization
			13.2.3 One-dimensional optimization examples
				13.2.3.1 Maximum of the black body radiation
		13.3 Multidimensional Optimization
			13.3.1 Examples of multidimensional optimization
				13.3.1.1 The inversed sinc function
				13.3.1.2 Three-dimensional optimization
				13.3.1.3 Joining two functions smoothly
				13.3.1.4 Hanging weights problem
		13.4 Combinatorial Optimization
			13.4.1 Backpack problem
			13.4.2 Traveling salesman problem
				13.4.2.1 Permutation generating algorithm
				13.4.2.2 Combinatorial solution of the traveling salesman problem
		13.5 Simulated Annealing Algorithm
			13.5.1 The backpack problem solution with the annealing algorithm
		13.6 Genetic Algorithm
		13.7  Self-Study
	14: Ordinary Differential Equations
		14.1 Introduction to Ordinary Differential Equation
		14.2 Boundary Conditions
		14.3 Numerical Method to Solve ODEs
			14.3.1 Euler's method
			14.3.2 The second-order Runge–Kutta method (RK2)
			14.3.3 The fourth-order Runge-Kutta method (RK4)
			14.3.4 Other numerical solvers
		14.4 Stiff ODEs and Stability Issues of the Numerical Solution
		14.5 MATLAB's Built-In ODE Solvers
		14.6 ODE Examples
			14.6.1 Free fall example
			14.6.2 Motion with the air drag
		14.7 Self-Study
	15: Discrete Fourier Transform
		15.1 Fourier Series
			15.1.1 Example: Fourier series for |t|
			15.1.2 Example: Fourier series for the step function
			15.1.3 Complex Fourier series representation
			15.1.4 Non-periodic functions
		15.2 Discrete Fourier Transform (DFT)
		15.3 MATLAB's DFT Implementation and Fast Fourier Transform (FFT)
		15.4 Compact Mathematical Notation for Fourier Transforms
		15.5 DFT Example
		15.6 Self-Study
	16: Digital Filters
		16.1 Nyquist Frequency and the Minimal Sampling Rate
			16.1.1 Undersampling and aliasing
		16.2 DFT Filters
			16.2.1 Low-pass filter
			16.2.2 High-pass filter
			16.2.3 Band-pass and band-stop filters
		16.3 Filter's Artifacts
		16.4 Windowing Artifacts
		16.5  Self-Study
References
Index