First Course in Scientific Computing

This book offers a new approach to introductory scientific computing. It aims to make students comfortable using computers to do science, to provide them with the computational tools and knowledge they need throughout their college careers and into their professional careers, and to show how all the pieces can work together. Rubin Landau introduces the requisite mathematics and computer science in the course of realistic problems, from energy use to the building of skyscrapers to projectile motion with drag. He is attentive to how each discipline uses its own language to describe the same concepts and how computations are concrete instances of the abstract.

Landau covers the basics of computation, numerical analysis, and programming from a computational science perspective. The first part of the printed book uses the problem-solving environment Maple as its context, with the same material covered on the accompanying CD as both Maple and Mathematica programs; the second part uses the compiled language Java, with equivalent materials in Fortran90 on the CD; and the final part presents an introduction to LaTeX replete with sample files.

Providing the essentials of computing, with practical examples, A First Course in Scientific Computing adheres to the principle that science and engineering students learn computation best while sitting in front of a computer, book in hand, in trial-and-error mode. Not only is it an invaluable learning text and an essential reference for students of mathematics, engineering, physics, and other sciences, but it is also a consummate model for future textbooks in computational science and engineering courses.

• A broad spectrum of computing tools and examples that can be used throughout an academic career

• Practical computing aimed at solving realistic problems

• Both symbolic and numerical computations

• A multidisciplinary approach: science + math + computer science

• Maple and Java in the book itself; Mathematica, Fortran90, Maple and Java on the accompanying CD in an interactive workbook format

Auteur
Rubin H. Landau is Distinguished Professor of Physics and Director of the Computational Physics Program at Oregon State University. He is the lead author of Computational Physics: Problem Solving with Computers; A Scientist's and Engineer's Guide to Workstations and Supercomputers; and Quantum Mechanics II: A Second Course in Quantum Theory.

Résumé
Studies of animal behavior have often been invoked to help explain and even guide human behavior. Think of Pavlov and his dogs or Goodall and her chimps. But, as these examples indicate, the tendency has been to focus on &quote;higher,&quote; more cognitively developed, and thus, it is thought, more intelligent creatures than mindless, robotic insects. Not so! Learn here how honeybees work together to form a collective intelligence and even how they make decisions democratically. The wizzzzdom of crowds indeed! Here are five habits of effective groups that we can learn from these clever honeybees. Princeton Shorts are brief selections excerpted from influential Princeton University Press publications produced exclusively in eBook format. They are selected with the firm belief that while the original work remains an important and enduring product, sometimes we can all benefit from a quick take on a topic worthy of a longer book. In a world where every second counts, how better to stay up-to speed on current events and digest the kernels of wisdom found in the great works of the past? Princeton Shorts enables you to be an instant expert in a world where information is everywhere but quality is at a premium. The Five Habits of Highly Effective Honeybees (and What We Can Learn from Them) does just that.

Contenu

List of Figures xv
List of Tables xix
Preface xxi
Chapter 1. Introduction 1
1.1 Nature of Scientific Computing 1
1.2 Talking to Computers 2
1.3 Instructional Guide 4
1.4 Exercises to Come Back To 6
PART 1. MAPLE (OR MATHEMATICA) BY DOING 7
Chapter 2. Getting Started with Maple 9
2.1 Setting Up Your Work Space 9
2.2 Maple's Problem-Solving Environment 10
2.3 Maple's Command Structure 14
2.4 Sums and sums 16
2.5 Execution Groups 21
2.6 Key Words and Concepts 22
2.7 Supplementary Exercises 23
Chapter 3. Numbers, Expressions, Functions; Rocket Golf 25
3.1 Problem: Viewing Rocket Golf 25
3.2 Theory: Einstein's Special Relativity 26
3.3 Math: Integer, Rational and Irrational Numbers 27
3.4 CS: Floating-Point Numbers 29
3.5 Complex Numbers 31
3.6 Expressions 32
3.7 Assignment Statements 34
3.8 Equality (rhs, lhs) 36
3.9 Functions 36
3.10 User-Defined Functions 39
3.11 Reexpressing Answers 39
3.12 CS: Overflow, Underflow, and Round-Off Error 44
3.13 Solution: Viewing Rocket Golf 45
3.14 Extension: Tachyons* 50
3.15 Key Words and Concepts 51
3.16 Supplementary Exercises 51
Chapter 4. Visualizing Data, Abstract Types; Electric Fields 55
4.1 Why Visualization? 55
4.2 Problem: Stable Points in Electric Fields 56
4.3 Theory: Stability Criteria and Potential Energy 56
4.4 Basic 2-D Plots: plot 58
4.5 Compound (Abstract) Data Types: [Lists] and {Sets }
63
4.6 3-D (Surface) Plots of Analytic Functions 69
4.7 Solution: Dipole and Quadrupole Fields 73
4.8 Exploration: The Tripole 76
4.9 Extension: Yet More Plot Types* 76
4.10 Visualizing Numerical Data 91
4.11 Plotting a Matrix: matrixplot* 97
4.12 Animations of Data* 102
4.13 Key Words and Concepts 104
4.14 Supplementary Exercises 105
Chapter 5. Solving Equations, Differentiation; Towers 107
5.1 Problem: Maximum Height of a Tower 107
5.2 Model: Block Stacking 107
5.3 Math: Equations as Challenges 109
5.4 Solving a Single Equation: solve, fsolve 110
5.5 Solving Simultaneous Equations (Sets) 113
5.6 Solution to Tower Problem 115
5.7 Differentiation: limit, diff, D 117
5.8 Numerical Derivatives* 126
5.9 Alternate Solution: Maximum Tower Height 127
5.10 Assessment and Exploration 128
5.11 Auxiliary Problem: Nonlinear Oscillations 129
5.12 Key Words and Concepts 131
5.13 Supplementary Exercises 131
Chapter 6. Integration; Power and Energy Usage (Also 14) 134
6.1 Problem: Relating Power and Energy Usage 134
6.2 Empirical Models 134
6.3 Theory: Power and Energy Definitions 136
6.4 Maple: Tools for Integration 136
6.5 Problem Solution: Energy from Power 139
6.6 Key Words and Concepts 143
6.7 Supplementary Exercises 144
Chapter 7. Matrices and Vectors; Rotation 145
7.1 Problem: Rigid-Body Rotation 145
7.2 Math: Vectors and Matrices 147
7.3 Theory: Angular Momentum Dynamics 149
7.4 Maple: Linear Algebra Tools 151
7.5 Matrix Arithmetic and Operations 157
7.6 Solution: Rotating Rigid Bodies 171
7.7 Exploration: Principal Axes of Rotation* 176
7.8 Key Words and Concepts 181
7.9 Supplementary Exercises 182
Chapter 8. Searching, Programming; Dipsticks 184
8.1 Problem: Volume of Liquid in Spherical Tanks 184
8.2 Math: Volume Integration 184
8.3 Algorithm: Bisection Searches 185
8.4 Programming in Maple 187
8.5 Solution: Volume from Dipstick Height 194
8.6 Key Words and Concepts 195
8.7 Supplementary Exercises 196
PART 2. JAVA (OR FORTRAN90) BY DOING 197
Chapter 9. Getting Started with Java 199
9.1 Compiled Languages 199
9.2 Java Program Pieces 201
9.3 Entering and Running Your First Program 202
9.4 Looking Inside Area.java 205
9.5 Key Words 207
9.6 Supplementary Exercises 207
Chapter 10. Data Types, Limits, Methods; Rocket Golf 208
10.1 Problem and Theory (Same as Chapter 3) 208
10.2 Java's Primitive Data Types 208
10.3 Methods (Functions) and Modular Programming 215
10.4 Solution: Viewing Rocket Golf 219
10.5 Your Problem: Modify Golf…