A First Course in Scientific Computing

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1 A First Course in Scientific Computing Symbolic, Graphic, and Numeric Modeling Using Maple, Java, Mathematica, and Fortran90 RUBIN H. LANDAU Contributors: Robyn Wangberg (Mathematica), Kyle Augustson (Fortran90), M. J. Paez, C. C. Bordeianu, C. Barnes PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD

2 Contents List of Figures List of Tables Preface xv xix xxi Chapter 1. Introduction Nature of Scientific Computing Talking to Computers Instructional Guide Exercises to Come Back To 6 PART 1. MAPLE (OR MATHEMATICA) BY DOING 7 Chapter 2. Getting Started with Maple Setting Up Your Work Space Maple's Problem-Solving Environment Maple's Command Structure Sums and sums Execution Groups Key Words and Concepts Supplementary Exercises 23 Chapter 3. Numbers, Expressions, Functions; Rocket Golf Problem: Viewing Rocket Golf Theory: Einstein's Special Relativity Math: Integer, Rational and Irrational Numbers CS: Floating-Point Numbers Complex Numbers Expressions Assignment Statements Equality (rhs, Ihs) 36

3 VIII CONTENTS 3.9 Functions User-Defined Functions Reexpressing Answers CS: Overflow, Underflow, and Round-Off Error Solution: Viewing Rocket Golf Extension: Tachyons* Key Words and Concepts Supplementary Exercises 51 Chapter 4. Visualizing Data, Abstract Types; Electric Fields Why Visualization? Problem: Stable Points in Electric Fields Theory: Stability Criteria and Potential Energy Basic 2-D Plots: plot Compound (Abstract) Data Types: [Lists] and {Sets} D (Surface) Plots of Analytic Functions Solution: Dipole and Quadrupole Fields Exploration: The Tripole Extension: Yet More Plot Types* Visualizing Numerical Data Plotting a Matrix: matrixplot* Animations of Data* Key Words and Concepts Supplementary Exercises 105 Chapter 5. Solving Equations, Differentiation; Towers Problem: Maximum Height of a Tower Model: Block Stacking Math: Equations as Challenges Solving a Single Equation: solve, fsolve Solving Simultaneous Equations (Sets) Solution to Tower Problem Differentiation: limit, diff, D Numerical Derivatives* Alternate Solution: Maximum Tower Height Assessment and Exploration Auxiliary Problem: Nonlinear Oscillations Key Words and Concepts Supplementary Exercises 131 Chapter 6. Integration; Power and Energy Usage (Also 14) Problem: Relating Power and Energy Usage Empirical Models Theory: Power and Energy Definitions 136

4 CONTENTS ix 6.4 Maple: Tools for Integration Problem Solution: Energy from Power Key Words and Concepts Supplementary Exercises 144 Chapter 7. Matrices and Vectors; Rotation Problem: Rigid-Body Rotation Math: Vectors and Matrices Theory: Angular Momentum Dynamics Maple: Linear Algebra Tools Matrix Arithmetic and Operations Solution: Rotating Rigid Bodies Exploration: Principal Axes of Rotation* Key Words and Concepts Supplementary Exercises 182 Chapter 8. Searching, Programming; Dipsticks Problem: Volume of Liquid in Spherical Tanks Math: Volume Integration Algorithm: Bisection Searches Programming in Maple Solution: Volume from Dipstick Height Key Words and Concepts Supplementary Exercises 196 PART 2. JAVA (OR FORTRAN90) BY DOING 197 Chapter 9. Getting Started with Java Compiled Languages Java Program Pieces Entering and Running Your First Program Looking Inside Area.java Key Words Supplementary Exercises 207 Chapter 10. Data Types, Limits, Methods; Rocket Golf Problem and Theory (Same as Chapter 3) Java's Primitive Data Types Methods (Functions) and Modular Programming Solution: Viewing Rocket Golf Your Problem: Modify Golf.java Coercion and Overloading* Keywords 229

5 X CONTENTS 10.8 Supplementary Exercises 229 Chapter 11. Visualization with Java, Classes, Packages D Graphs within Java: PtPlot Installing PtPlot: See Appendix C* Classes and Packages* Gnuplot Basics Java Archives: jar* 244 Chapter 12. Flow Control via Logic; Projectiles Problem: Frictionless Projectile Motion Theory: Kinematics Computer Science: Designing Structured Programs Flow Control via Logic Implementation: Projectile.java Solution: Projectile Trajectories Keywords Supplementary Exercises 260 Chapter 13. Java Input and Output* Basic Input with Scanner Streams: Standard Output, Input, and Error I/O Exceptions: FileCatchThrow.java Automatic Code Documentation: javadoc Nonstandard Formatted Output: printf 275 Chapter 14. Numerical Integration; Power and Energy Usage Problem (Same as Chapter 6): Power and Energy Algorithms: Trapezoid and Simpson's Rules Assessment: Which Rule Is Better? Key Words and Concepts Supplementary Exercises 289 Chapter 15. Differential Equations with Java and Maple* Problem: Projectile Motion with Drag Model: Velocity-Dependent Drag Algorithm: Numerical Differentiation Math: Solving Differential Equations Assessment: Balls Falling Out of the Sky? Maple: Differential-Equation Tools Maple Solution: Drag oc Velocity Extract Operands Drag oc v 2 (Exercise) Dragocu 3 / 2 306

6 CONTENTS XI Exploration: Planetary Motion* Keywords Supplementary Exercises 311 Chapter 16. Object-Oriented Programming; Complex Currents Problem: Resonance in RLC Circuit Math: Complex Numbers Theory: Resistance Becomes Impedance CS: Abstract Data Types, Objects Java Solution: Complex Currents Maple Solution: Complex Currents Explorations: OOP Worked Examples* Keywords Java and Maple Exercises 340 Chapter 17. Arrays: Vectors, Matrices; Rigid-Body Rotations Problem: Rigid-Body Rotations Theory: Angular-Momentum Dynamics CS, Math: Arrays, Vectors, and Matrices Implementation: Inertia.java, lnertia3d.java Jama: Java Matrix Library* Keywords Supplementary Exercises 353 Chapter 18. Advanced Objects; Baton Projectiles* Problem: Trajectory of Thrown Baton Theory: Combined Translation and Rotation CS: OOP Design Concepts Keywords Supplementary Exercises 377 Chapter 19. Discrete Math, Arrays as Bins; Bug Dynamics* Problem: Variability of Bug Populations Theory: Self-Limiting Growth, Discrete Maps Assessment: Properties of Nonlinear Maps Exploration: Bifurcation Diagram, BugSort.java* Exploration: Other Discrete Maps* 384 Chapter D Arrays: File I/O, PDEs; Realistic Capacitor Problem: Field of Realistic Capacitor Theory and Model: Electrostatics and PDEs Algorithm: Finite Differences Implementation: Laplace.Java Exploration: 2-D Capacitor 391

7 XII CONTENTS 20.6 Exploration: 3-D Capacitor* Key Words 393 Chapter 21. Web Computing, Applets, Primitive Graphics What Is Web Computing? Implementation: Get This to Work First Exploration: Modify Appleti.Java Extension: PtPlot as Applet* Extension: Applet with Button Input* Extension: AWT, JFC, and Swing* Example: Baton Applet, Jparabola.java* Keywords Supplementary Exercises 410 PART 3. TEX SURVIVAL GUIDE 411 Chapter 22. l^tgx for Text Why I5TEX? Structure of a I^T^X Document Sample Input File (Sample.tex) Sample l5tgx Output Fonts for Text Environments Lists Sections 425 Chapter 23. IflgX for Mathematics Entering Mathematics: Math Mode Mathematical Symbols and Greek Math Accents Superscripts and Subscripts Calculus and Sums Changing Math Fonts Math Functions Fractions Roots Brackets (Delimiters) Multiline Equations Matrices and Math Arrays Including Graphics Exercise: Putting It All Together 438 Appendix A. Glossary 441

8 CONTENTS xiii Appendix B. Maple Quick Reference, Debugging Help 450 Appendix C. Java Quick Reference and Installing Software 461 C.1 Java Elements 461 C.2 Transferring Files from the CD 465 C.3 Using our Maple Worksheets 466 C.4 Using our Java Programs 466 C.5 Installing PtPlot (or Other) Packages 467 C.6 Installing Java Developer's Kit 469 Bibliography 471 Index 477

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