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1 Engineering Problem Solving 1 1.1 Problem-Solving Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 ProblemSolving Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Computing Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Computin g Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Matlab Technical Computing Environment 14 2.1 Workspace,Windows, and Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 ScalarMathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 BasicMathematical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 Computational Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5 Display Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Accuracyand Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 Files and File Management 37 3.1 FileManagement Definitions and Commands . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Saving and RestoringMatlab Information . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 ScriptM-Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4 Errors and Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.5 Matlab Search Path, PathManagement, and Startup . . . . . . . . . . . . . . . . . . 49 i 4 Trigonometry and ComplexNum bers 51 4.1 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.3 Two-Dimensional Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 Arrays and Array Operations 81 5.1 Vector Array s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Matrix Array s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.3 ArrayPlotting Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6 Mathematical Functions and Applications 101 6.1 Signal Representation, Processing, and Plotting . . . . . . . . . . . . . . . . . . . . . 101 6.2 Poly nomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3 Partial Fraction Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.4 Functions of Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.5 User-Defined Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.6 Plotting Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7 DataAnalysis 135 7.1 Maximum andMinimum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.2 Sums and Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.3 Statistical Analy sis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 7.4 Random Number Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 8 Selection Programming 155 8.1 Relational and Logical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.2 Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.3 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.4 Selection Statements in User-Defined Functions . . . . . . . . . . . . . . . . . . . . . 169 8.5 Update Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 ii 8.6 Applied ProblemSolving: Speech Signal Analy sis . . . . . . . . . . . . . . . . . . . . 175 9 Vectors, Matrices and Linear Algebra 180 9.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 9.2 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 9.3 Solutions to Sy stems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . 196 9.4 Applied ProblemSolving: RobotMotion . . . . . . . . . . . . . . . . . . . . . . . . . 202 10 Curve Fitting and Interpolation 207 10.1 MinimumMean-Square Error Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . 207 10.2 Applied Problem Solving: Hydraulic Engineering . . . . . . . . . . . . . . . . . . . . 213 10.3 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 10.4 Applied ProblemSolving: Human Hearing . . . . . . . . . . . . . . . . . . . . . . . . 219 11 Integration and Differentiation 223 11.1 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11.2 Numerical Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 12 Strings, Time, Base Conversion and Bit Operations 239 12.1 Character Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 12.2 Time Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 12.3 Base Conversions and Bit Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 13 Symbolic Processing 250 13.1 Sy mbolic Expressions and Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 13.2 Manipulating Trigonometric Expressions . . . . . . . . . . . . . . . . . . . . . . . . . 257 13.3 Evaluating and Plotting Sy mbolic Expressions . . . . . . . . . . . . . . . . . . . . . 258 13.4 Solving Algebraic and Transcendental Equations . . . . . . . . . . . . . . . . . . . . 259 13.5 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 13.6 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
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