Problem Solving with Fortran 90 : For Scientists and Engineers

This book provides students with an introduction to Fortran 90, one of the most powerful and flexible programming languages for scientific computation available today. The author shows how using computers and Fortran 90 it is possible to tackle and solve a wide range of problems as they might be encountered in engineering or in the physical sciences. Following a brief introduction to computing in general, the author presents a thorough guide to problem-solving and algorithm design using pseudo-code to develop an understanding of the steps that need to be taken to solve a particular problem. Subsequent chapters introduce the main features of Fortran 90 motivated by particular ideas and tasks that are typically found in science and engineering

1. Computing Environments for Problem Solving.- 1.1 A Brief History of Electronic Computing.- 1.1.1 The First Generation.- 1.1.2 The Second and Third Generations.- 1.1.3 The Fourth Generation.- 1.2 The Academic Computing Environment.- 1.2.1 The Department-Based Computing Environment.- 1.2.2 The Personal Computing Environment.- 1.3 What Do You Need to Know About Your Computing Environment?.- 1.4 Fortran and the Personal Computing Environment.- 1.5 Is Programming Necessary Anymore?.- 1.6 Exercises.- 2. Solving Problems with a High-Level Programming Language.- 2.1 Structured Programming and Problem Solving.- 2.1.1 A High-Level Programming Language Provides the Tool.- 2.1.2 Developing a Formal Approach to Problem Solving.- 2.1.3 Beware of Logical Errors.- 2.2 Designing Algorithms for Procedural Programming Languages.- 2.2.1 Getting Started.- 2.2.2 Executable Instructions.- 2.2.3 Data Types and Variables.- Data types.- Variables.- 2.2.4 Designing Algorithms for Solving Problems.- Defining a pseudocode language.- The three basic program control structures.- Adding to your pseudocode vocabulary.- Flowcharts: another way to visualize algorithms.- 2.3 Program Modularization.- 2.4 Applications.- 2.4.1 Maximum Deflection of a Beam Under Load.- 2.4.2 Oscillating Frequency of an LC Circuit.- 2.5 Debugging Your Algorithms.- 2.5.1 Algorithm Style.- 2.5.2 Problems with Your Algorithms.- 2.6 Exercises.- 2.6.1 Self-Testing Exercises.- 2.6.2 Basic Algorithm Development Exercises.- 2.6.3 Algorithm Development Applications.- 3. Getting Started with Fortran: Writing Simple Programs.- 3.1 A Simple Problem and a Fortran Program to Solve It.- 3.2 Program Layout.- 3.2.1 What Is “Source Code?”.- 3.2.2 Where Does Source Code Come From?.- 3.2.3 Why Do the Fortran Statements All Start in Column 7?.- 3.2.4 Inserting Comments in Source Code Files.- 3.2.5 How Much of P-3.1 Is Absolutely Necessary and How Much Is a Matter of Style?.- 3.2.6 Fortran Keywords.- 3.2.7 What If a Statement Is Too Long to Fit on a Single Line?.- 3.2.8 Executable and Nonexecutable Statements.- 3.3 Declaring Variables and Defining Constants.- 3.3.1 Variable Names and Data Type Declarations.- 3.3.2 Intrinsic Data Types.- Type declarations for intrinsic data types.- Type declarations for numbers.- Type declarations for logical variables.- Type declarations for characters and strings of characters.- The PARAMETER attribute and statement.- Enforcing explicit typing.- The implications of type declaration.- Using nonexecutable statements in programs.- 3.3.3 Constants.- Integers and real numbers.- Logical constants.- Character constants.- 3.3.4 Initializing Values with the DATA Statement.- 3.4 List-Directed Input and Output.- 3.4.1 Reading and Displaying Numerical Values.- Displaying a prompt for user input.- Getting input from the keyboard.- Displaying output.- 3.4.2 Manipulating Text Information.- 3.5 Arithmetic Operators, Assignment Statements, and Calculations.- 3.5.1 Arithmetic Operators, Expressions, and the Assignment Operator.- 3.5.2 Assignment Statements That Increment Variables.- 3.5.3 Mixed-Mode Calculations.- 3.5.4 Using Compatible Constants.- 3.5.5 Operator Precedence.- 3.6 Program Termination.- 3.7 Compiling and Executing a Program.- 3.7.1 Source Code Portability.- 3.7.2 Compilation and Execution.- 3.7.3 Saving Output from Your Programs.- 3.8 Applications.- 3.8.1 Maximum Deflection of a Beam Under Load.- 3.8.2 Relativistic Mass and Speed of an Electron.- 3.9 Debugging Your Programs.- 3.9.1 Programming Style.- 3.9.2 Your Programs Will Often Contain Errors.- 3.9.3 Some Common Errors.- Compilation Errors.- Execution Errors.- Logical Errors.- 3.9.4 Forcing Your Programs to Fail.- 3.10 Exercises.- 3.10.1 Self-Testing Exercises.- 3.10.2 Basic Programming Exercises.- 3.10.3 Programming Applications.- 4. Using Functions to Expand the Power of Fortran.- 4.1 Fortran Intrinsic Functions.- 4.1.1 Intrinsic Functions for Arithmetic Calculations: Arguments and Ranges.- 4.1.2 Intrinsic Functions for Character and String Manipulation.- 4.1.3 Examples of Calculations Using Intrinsic Functions.- Polar/Cartesian conversions.- Calculating the absolute value.- The remainder from integer or real division.- 4.2 Fortran Statement Functions.- 4.3 Applications.- 4.3.1 Refraction of Light.- 4.3.2 Inverse Hyperbolic Functions.- 4.4 Debugging Your Programs.- 4.4.1 Programming Style.- 4.4.2 Problems with Programs.- 4.5 Exercises.- 4.5.1 Self-Testing Exercises.- 4.5.2 Basic Programming Exercises.- 4.5.3 Programming Applications.- 5. Gaining Control Over Program Output.- 5.1 The Formatted PRINT Statement.- 5.1.1 Introduction to Formatted Output.- 5.1.2 Format Descriptors for Numbers and Character Strings.- INTEGER descriptors.- REAL descriptors.- CHARACTER descriptors.- LOGICAL descriptor.- General descriptor.- String constant descriptors.- 5.1.3 Control Descriptors.- Carriage control.- Skipping spaces.- Sign display.- New lines.- Tabulation.- Format termination.- 5.1.4 Repeating Groups of Descriptors.- 5.1.5 Producing Formatted Output Without a FORMAT Statement.- 5.2 The WRITE Statement.- 5.2.1 Syntax of the WRITE Statement and the Standard Output Unit.- 5.2.2 Format Descriptors for the WRITE Statement.- 5.3 Saving Program Output.- 5.4 Applications.- 5.4.1 Stellar Magnitude and Distance.- 5.4.2 Relativistic Mass and Speed of an Electron.- 5.5 Debugging Your Programs.- 5.5.1 Programming Style.- 5.5.2 Problems with Programs.- 5.6 Exercises.- 5.6.1 Self-Testing Exercises.- 5.6.2 Basic Programming Exercises.- 5.6.3 Programming Applications.- 6. Program Control: Branching and Repetitive Calculations.- 6.1 Using Program Control Structures.- 6.1.1 The IF…THEN…(ELSE…) Pseudocode Construct.- 6.1.2 The CHOOSE Pseudocode Command.- 6.1.3 The LOOP…END LOOP Pseudocode Command.- Count-controlled loops.- Conditional loops.- 6.2 Relational and Logical Operators and the Fortran IF… Construct.- 6.2.1 Relational and Logical Operators.- 6.2.2 The IF… Construct.- 6.2.3 Using the IF… Construct in Programs.- 6.3 The SELECT CASE Construct.- 6.4 Fortran Loop Constructs.- 6.4.1 Count-Controlled (DO… ) Loops.- 6.4.2 Pre- and Post-Test Conditional Loop Constructs.- Pre-test loops.- Post-test loops.- 6.4.3 Nested Loops.- 6.4.4 Loop Design Considerations.- 6.5 Using Implied DO… Loops in Output Statements.- 6.6 Applications.- 6.6.1 Refraction of Light.- 6.6.2 Oscillating Frequency of an LC Circuit.- 6.6.3 Calculating Radiation Exposures for a Materials Testing Experiment.- 6.6.4 Maximum Deflection of a Beam with Various Support/Loading Systems.- 6.7 Debugging Your Programs.- 6.7.1 Programming Style.- 6.7.2 Logical Problems.- 6.7.3 Syntax and Execution Problems.- 6.8 Exercises.- 6.8.1 Self-Testing Exercises.- 6.8.2 Basic Programming Exercises.- 6.8.3 Programming Applications.- 7. Program Modularization.- 7.1 Designing Modularized Algorithms with the CALL and SUBPROGRAM Pseudocode Commands.- 7.2 Fortran Subroutines.- 7.2.1 Using Subroutines.- 7.2.2 Controlling the Flow of Information.- Expressing intent.- Enforcing intent.- 7.2.3 More About SUBROUTINE Syntax.- 7.3 Fortran Functions.- 7.4 Using Subroutines and Functions.- 7.4.1 Using the MODULE Structure for Passing Information to Subroutines and Functions.- 7.4.2 Initializing Information in Subroutines and Functions.- 7.4.3 Using Subroutines and Functions in Argument and Parameter Lists.- 7.4.4 Choosing Between Subroutines and Functions.- 7.5 Applications.- 7.5.1 Relativistic Mass and Speed of an Electron.- 7.5.2 A Function Library for Converting Units.- 7.5.3 A Simple Character-Based Function Plotter.- 7.6 Debugging Your Programs.- 7.6.1 Programming Style.- 7.6.2 Problems with Programs.- 7.7 Exercises.- 7.7.1 Self-Testing Exercises.- 7.7.2 Basic Programming Exercises.- 7.7.3 Programming Applications.- 8. Using Arrays to Organize Information.- 8.1 Arrays in Structured Programming.- 8.2 Basic Array Implementation.- 8.2.1 Example: Testing a Random Number Generator.- 8.2.2 Declaring Arrays.- 8.2.3 Assigning Values to Arrays.- Assigning a value to an entire array or part of an array.- Assigning array elements with count-controlled loops.- Assigning values to individual array elements.- Using a DATA statement to initialize arrays.- Using elemental intrinsic functions.- 8.2.4 Displaying the Contents of Arrays (Implied DO… Loops).- 8.2.5 Example: Monthly Ozone Summary.- 8.3 Using Statically Allocated Arrays in Subprograms.- 8.4 Allocatable Arrays.- 8.5 Treating Strings of Characters as Arrays of Characters.- 8.6 The TYPE Statement, Records, and Arrays of Records.- 8.7 Applications.- 8.7.1 Vector Operations.- 8.7.2 Cellular Automata and Sierpinski Triangles.- 8.7.3 Probability Analysis for Quality Control of Manufacturing Processes.- 8.8 Debugging Your Programs.- 8.8.1 Programming Style.- 8.8.2 Problems with Programs That Use Arrays.- 8.9 Exercises.- 8.9.1 Self-Testing Exercises.- 8.9.2 Basic Programming Exercises.- 8.9.3 Programming Applications.- 9. Using Formatted Sequential Access and Internal Files.- 9.1 The Text File Concept.- 9.2 OPEN, READ, and CLOSE Statements for Sequential File Access.- 9.2.1 Reading a File Containing Student Names and Grades.- 9.2.2 The OPEN and REWIND Statements.- 9.2.3 The READ and BACKSPACE Statements.- 9.2.4 The CLOSE Statement.- 9.3 Files and Arrays.- 9.4 More About Formatted READ Statements.- 9.4.1 FORMAT Statements and Standard Field Descriptors.- 9.4.2 Reading Internal Files.- 9.5 Writing Text Files.- 9.6 Applications.- 9.6.1 Exponential Smoothing of Data.- 9.6.2 Billing Program for an Urban Water Utility.- 9.6.3 Merging Sorted Lists.- 9.6.4 Creating a “Quote-and-Comma-Delimited” Input File for Spreadsheets.- 9.7 Debugging Your Programs.- 9.7.1 Programming Style.- 9.7.2 Problems with Programs That Access External Data Files.- 9.8 Exercises.- 9.8.1 Self-Testing Exercises.- 9.8.2 Basic Programming Exercises.- 9.8.3 Programming Applications.- 10. Some Essential Programming Algorithms.- 10.1 Introduction.- 10.2 Searching Algorithms.- 10.2.1 Linear Searches.- 10.2.2 Binary Search.- 10.2.3 Comparing Searching Algorithms.- 10.2.4 A Driver Program for Testing Searching Algorithms.- 10.3 Sorting Algorithms.- 10.3.1 Selection Sort.- 10.3.2 Insertion Sort.- 10.3.3 Efficiency of Sorting Algorithms.- 10.3.4 A Driver Program for Testing Sorting Algorithms.- 10.4 Recursive Algorithms.- 10.5 The Recursive Quicksort Algorithm.- 10.6 Applications.- 10.6.1 Keeping a List of Words in Alphabetical Order.- 10.6.2 Evaluating Legendre Polynomials.- 10.7 Debugging Your Programs.- 10.7.1 Programming Style.- 10.7.2 Problems with Programs.- 10.8 Exercises.- 10.8.1 Self-Testing Exercises.- 10.8.2 Basic Programming Exercises.- 10.8.3 Programming Applications.- 11. Basic Statistics and Numerical Analysis with Fortran.- 11.1 Introduction.- 11.2 Basic Descriptive Statistics.- 11.2.1 The Sample Mean and Standard Deviation.- 11.2.2 Linear Regression and the Linear Correlation Coefficient.- 11.3 Numerical Differentiation.- 11.3.1 Newton’s and Stirling’s Formulas.- 11.3.2 Application. Estimating the Speed of a Falling Object.- 11.4 Numerical Integration.- 11.4.1 Polynomial Approximation Methods.- 11.4.2 Application: Evaluating the Gamma function.- 11.5 Solving Systems of Linear Equations.- 11.5.1 Linear Equations and Gaussian Elimination.- 11.5.2 Application: Current Flow in a DC Circuit with Multiple Resistive Branches.- 11.6 Finding the Roots of Equations.- 11.7 Numerical Solutions to Differential Equations.- 11.7.1 Motion of a Damped Mass and Spring.- 11.7.2 Application. Current Flow in a Series LRC Circuit.- 11.8 Exercises.- 11.8.1 Basic Programming Exercises.- 11.8.2 Programming Applications.- 12. A Closer Look.- 12.1 Introduction.- 12.2 Using More Than One Program Unit.- 12.2.1 Merging Source Code.- 12.2.2 Merging Object Code.- 12.3 The Internal Representation of Numbers and Extended Precision.- 12.3.1 Internal Representation of Numbers.- Integers.- Real Numbers.- 12.3.2 Specifying Precision for Numerical Variables.- 12.4 Array Operations and Array Inquiry and Reduction.- 12.4.1 Intrinsic Array Operations.- 12.4.2 Array Functions.- Array multiplication functions.- Array inquiry functions.- Array reduction functions.- 12.5 Direct Access and Unformatted (Binary) Files.- 12.5.1 Introduction to File Types.- 12.5.2 Using Other File Types.- 12.5.3 Example: Binary Search of a File.- 12.6 The COMPLEX Data Type.- 12.7 Data Sharing With COMMON Blocks.- Appendices.- Appendix 1. Table of ASCII Characters for IBM-Compatible PCs.- Appendix 2. Summary of Pseudocode Commands and Fortran Statement Syntax.- Appendix 2.1 Pseudocode Commands.- Appendix 2.2 Fortran Statement Syntax.- Appendix 3. Source Code File Name Summary.- Appendix 4. Accessing the System Time and Date.