CONTENTS vii 10 A Potpourri of Applications 267 l0.1 Finding a zero using the“binary chop” 267 11 Programming in MATLAB 271 11.1 A taste of MATLAB 271 11.2 Arrays in Matlab.. 273 11.3L0ops..·· 279 11.3.1 The for loop.·· 279 11.3.2 The while loop 282 1l.4 The if/else construct·· 282 11.5 Some Matlab terminology 283 11.6 Operators in MATLAB..... 284 11.6.1 Math operators in Matlab 284 11.7 Pointwise operators in MATLAB 285 11.7.1 Logical Operators in Matlab 286 11.8M-fles.········· 288 11.8.1 Script M-files 288 11.8.2 Function M-files ... 292 11.9 Problems........ 295 11.10Projects 327 11.10.1Supplementary material:Trajectories without air resistance 346 11.10.2Supplementary material:Trajectories with air resistance ...... 346 11.10.3Supplementary material:Stepping algorithms ............ 347 11.10.4Supplementary material:Trajectories of objects in the universe... 354 11.10.5Supplementary material:Stepping algorithms...... 355 12 Graphics 367 12.1 Two Dimensional Plots.. 367 12.1.1 A basic plot...... 367 12.1.2 Using different line colors 367CONTENTS vii 10 A Potpourri of Applications 267 10.1 Find ing a zero using the “binary chop” . . . . . . . . . . . . . . . . . . . . . 267 11 Programming in MATLAB 271 11.1 A taste of MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 11.2 Arrays in Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 11.3 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 11.3.1 The for loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 11.3.2 The while loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 11.4 The if/else construct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 11.5 Some Matlab terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 11.6 Operators in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 11.6.1 Math operators in Matlab . . . . . . . . . . . . . . . . . . . . . . . . 284 11.7 Pointwise operators in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . 285 11.7.1 Logical Operators in Matlab . . . . . . . . . . . . . . . . . . . . . . . 286 11.8 M-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 11.8.1 Script M-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 11.8.2 Function M-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 11.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 11.10Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 11.10.1 Supplementary material: Trajectories without air resistance . . . . . 346 11.10.2 Supplementary material: Trajectories with air resistance . . . . . . . 346 11.10.3 Supplementary material: Stepping algorithms . . . . . . . . . . . . . 347 11.10.4 Supplementary material: Trajectories of objects in the universe . . . 354 11.10.5 Supplementary material: Stepping algorithms . . . . . . . . . . . . . 355 12 Graphics 367 12.1 Two Dimensional Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 12.1.1 A basic plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 12.1.2 Using d ifferent line colors . . . . . . . . . . . . . . . . . . . . . . . . 367