Physical Modeling in MATLAB (Downey)
- Page ID
- 119212
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1: Modeling and Simulation
- This chapter presents the modeling framework we’ll use in this book, introduces the MATLAB and Octave programming languages, and helps you debug some of the errors you are likely to make while you are getting started
- 2: Scripts
- This chapter introduces scripts, which are files that contain MATLAB/Octave code. It also presents variables, values, and the assignment statement
- 3: Loops
- This chapter presents the for loop, sequences, series, plotting, and a way of writing programs called incremental development
- 4: Vectors
- This chapter introduces vectors, which provide a way to store a sequence of values. And it presents common vector operators including reduce and apply
- 5: Functions
- This chapter discusses name collisions and an important tool for avoiding them: functions. It also explains input variables and function calls
- 7: Zero-finding
- This chapter presents conditional statements, which check for conditions and determine the behavior of programs. And it introduces a program development process called encapsulation and generalization
- 8: Functions of vectors
- This chapter introduces fzero, which is a MATLAB function that finds the zeros, or roots, of nonlinear equations. It also presents some tips that might help you with debugging
- 9: Ordinary Differential Equations
- This chapter combines two topics from previous chapters: vectors and functions. It presents functions that take vectors as input variables and return them as output variables. And it introduces logical vectors, which contain a sequence of true and false values.
- 10: Systems of ODEs
- This chapter uses a system of differential equations to simulate the interactions of predator and prey species and presents several ways to plot the results
- 11: Second-order systems
- This chapter describes Newtonian motion using a second-order differential equation and uses ode45 to simulate falling objects with and without air resistance
- 12: Two Dimensions
- This Chapter extends the methods from the previous chapter to simulate projectiles like baseballs. It introduces spatial vectors as a way to represent quantities with two and three dimensions
- 13: Optimization
- This chapter introduces fminsearch, which is a MATLAB function that searches for the maximum or minimum of a function.
- 14: Springs and Things
- Adds new forces to the toolkit, including spring forces and universal gravitation. It uses them to simulate the orbit of the Earth around the Sun.
- 15: Under the Hood
- This chapter reviews some of the MATLAB functions we’ve used—fzero, ode45, and fminsearch—and explains more about how they work.