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This book introduces the beginner to FORTRAN. To help the reader develop analysis skills while learning programming, engineering computations are incorporated with sound programming practices. Eight major Programming Assignments sections, each with a sample and solved model, illustrate the methods of preceding chapters, as well as introduce discussions concerning engineering orientation. This second edition successfully integrates numerous advanced topics in numerical methods as they relate to computational procedures in order to reinforce their application in other courses such as calculus and physics. Topics especially tailored to the beginning user include matrix equations, root of functions, curve-fitting, series expansions, integration and differentiation, and differential equations.

Dr. Garold (Gary) Joseph Borse (1940-2019) was born in Detroit, Michigan, and graduated from St. Rita's High School in 1958. Gary received his B.S. in Physics and Mathematics in 1962. Gary attended the University of Virginia on a National Defense Scholarship and received his M.S. in Physics in 1964 and Ph.D. in Physics in 1966. Gary began his career at Lehigh University as an assistant professor of physics in 1966 and spent the summer of 1967 and 1968 as a visiting scientist in the Department of Physics at Case Western Reserve University. He was promoted to associate professor at Lehigh University in 1971 and to full professor in 1976. He served as associate chairman and chairman of the department during his long tenure. Gary was a lifelong learner and had a passion for teaching. He delivered guest lectures at his children's schools and various other organizations sharing his love of the sciences. Gary always sought out adventure and was nominated by the National Academy of Sciences to the Czechoslovak Academy of Sciences as an exchange scientist from 1972 to 1973. He spent much of that year at the ČSAV Nuclear Research Institute at Řež (near Prague). Gary was a member of the American Physical Society and a contributing editor to PWS Publishing Company. He started his research career in theoretical structure of the nuclei and later developed an expertise in the area of mathematical and computational physics. He expanded his interests into computer programming and wrote several texts books about FORTRAN 77 and MATLAB. Gary was a contributing author to at least 25 research articles.

Preface
1. Computer Operations
1.1 Introduction
1.2 Operational Principles of Digital Computers
1.3 Communicating with the Computer
1.4 Computer Operating Systems: Getting Started on the Computer
1.5 Program ZERO
Summary
Problems
2. Fundamentals of FORTRAN
2.1 Introduction
2.2 Constants in FORTRAN
2.3 FORTRAN Variables
2.4 Arithmetic Expressions
2.5 More Complicated Arithmetic Expressions
2.6 Assignment Statement
2.7 Program ZERO
2.8 Translating Algebra into FORTRAN
2.9 Elementary Input and Output in FORTRAN Programs
Summary
Problems
3. Flow-Control Structures and Program Design
3.1 Introduction
3.2 Using Flowcharts and Pseudocode in Program Design
3.3 Decision Structures in FORTRAN
3.4 Loop Structures in FORTRAN
3.5 Good Programming Style
3.6 Additional Control Statements
Summary
Problems
A. Programming Assignment
A.1 Introduction
A.2 Sample Program
□ Civil Engineering: Pressure Drop in a Fluid Flowing through a Pipe
A.3 Programming Problems
□ Engineering Career Choices: Mechanical Engineering
□ A-A: Mechanical Engineering: Most Cost-Effective Steam Pipe Insulation
□ Engineering Career Choices: Civil Engineering
□ A-B: Civil Engineering: Oxygen Deficiency of a Polluted Stream
□ Engineering Career Choices: Industrial Engineering
□ A-C: Industrial Engineering: Cost Comparisons for Purchasing a Fleet of Cars
4. Elementary Programming Techniques
4.1 Introduction
4.2 Statement Function
4.3 Finding the Minimum and Maximum of a Set of Numbers
4.4 Performing a Summation
4.5 Bisection Technique for Finding Roots of Equation
4.6 Using Data Files and Data Statements
4.7 Using Direct-Access (DAM) Files
Summary
Problems
5. Subroutines and Functions
5.1 Introduction
5.2 Review of Statement Functions
5.3 Subroutine Subprograms
5.4 Function Subprograms
5.5 Sample Programs Using Functions and Subroutines
5.6 Constructing Modular Programs
5.7 Additional Features Available for Subprograms
Summary
Problems
B. Programming Assignment
B.1 Sample Program
□ Engineering Career Choices: Chemical Engineering
□ Sample Programming Problem: Separation of Two Liquids by Differential Distillation
B.2 Programming Problems
□ Engineering Career Choices: Materials Science and Metallurgical Engineering
□ B-A: Metallurgical Engineering: Carburization
□ Engineering Career Choices: Electrical Engineering
□ B-B: Electrical Engineering: Comparative Impedance of Two Transition Lines
□ B-C: Chemical Engineering/Chemistry: Coexistence of Liquids and Gases
6. Elementary Formatted Input-Output
6.1 Introduction
6.2 Formatted I/O Statements
6.3 FORMAT Statements
6.4 Using FORMAT Statements for Reading Data
6.5 Elementary Input and Output of Text
6.6 Additional Input/Output Features
Summary
Problems
7. Arrays and Subscripted Variables
7.1 Introduction
7.2 Array-Declaration Statements
7.3 Internal Storage of Arrays
7.4 Implied DO Loops
7.5 Arrays as Elements of an Argument List
7.6 Programming Techniques Using Arrays
Summary
Problems
C. Programming Assignment
C.1 Sample Problem
□ Industrial Engineering: Minimizing Repair Costs
C.2 Programming Problems
□ C-A: Chemical Engineering: Compressibility Factors for Real Gases
□ C-B: Minimum of a Multidimensional Array or Function
□ C-C: Mechanical Engineering: Cooling Fins on a Steam Pipe
□ C-D: Nim
8. Nonnumerical Applications: Character Variables
8.1 Introduction
8.2 Review of Character Variables
8.3 Character Substrings
8.4 Intrinsic Functions Used in Character Substring Operations
8.5 Character Expressions: Concatenation
8.6 Comparing Character Strings
Summary
Problems
9. Additional FORTRAN Features
9.1 Introduction
9.2 Additional Data Types Available in FORTRAN
9.3 Initializing Variables at Compilation Time
9.4 Order of FORTRAN Statements
9.5 DoWhile Structure in Extended FORTRAN
9.6 Additional FORTRAN Intrinsic Functions
9.7 Conclusion
Summary
Problems
D. Programming Assignment
D.1 Sample Program
□ Engineering Career Choices: Aeronautical/Aerospace Engineering
□ Sample Problem: Range of a Constant Thrust Rocket
D.2 Programming Problems
□ D-A: Chemical Engineering: Optimum Depth of a Fluidized-Bed Reactor
□ D-B: Electrical Engineering: A Double-Precision Root Solver
□ D-C: Electrical Engineering: Complex Numbers and AC Circuits
10. Taylor Series and Numerical Differentiation
10.1 Introduction
10.2 Taylor Series
10.3 Numerical Differentiation
10.4 Interpolation
Summary
Problems
11. Roots of Equations
11.1 Introduction
11.2 Refinement of the Bisection Method
11.3 Newton's Method for Root Solving
11.4 Rate of Convergence
11.5 Secant Method
11.6 Root-Solving Procedures for Polynomials
11.7 Comparison of Root-Solving Methods
Summary
Problems
E. Programming Assigngment
E.1 Sample Program
□ Mechanical Engineering: Cooling Curve for Transfer Ladle Cars
E.2 Programming Problems
□ E-A: Civil Engineering and Mechanics: Buckling of a Tall Mast
□ E-B: General Engineering: Functions Describing Diffusion
□ E-C: Chemistry/Chemical Engineering: Determining the Diffusion Constant
12. Linear Simultaneous Equations: Matrices
12.1 Introduction
12.2 Notation of Matrices
12.3 Determinants
12.4 Cramer's Rule
12.5 Gauss-Jordan Method of Solving Simultaneous Linear Equations
12.6 Matrix Inversion by the Gauss-Jordan Method
12.7 Relative Speed and Accuracy of the Various Matrix Algorithms
12.8 Iterative Techniques for Solving Simultaneous Equations
12.9 Miscellaneous FORTRAN Codes Relating to Matrices
Summary
Problems
F. Programming Assignment
F.1 Sample Program
□ Civil Engineering: Fluid Flow through a Plumbing Network
F.2 Programming Problems
□ F-A: Civil Engineering: Model of a Stress Calculation for a Bridge
□ F-B: Electrical Engineering: Currents in an Electrical Network
□ F-C: Calculating a Trajectory with Air Drag
13. Least Squares Curve Fitting
13.1 Introduction
13.2 Principles of Least Squares Analysis
13.3 Minimum or Maximum of a Function of Two Variables
13.4 Minimization of the Sum of the Squared Deviations
13.5 Least Squares Fit of a Polynomial
13.6 Validity of Fit
13.7 FORTRAN Code for a Polynomial Least Squares Curve Fit
13.8 Example of a Least Squares Polynomial Fit
13.9 Limitations of the Least Squares Procedures
13.10 Cubic Spline Fits
Summary
Problems
G. Programming Assignment
G.1 Sample Program
□ Chemistry/Chemical Engineering: Empirical Heat Capacities of Gases
G.2 Programming Problems
□ G-A: Aerodynamics: Free Fall in Air
□ G-B: Record Times for the Mile Run
14. Numerical Integration
14.1 Introduction
14.2 Trapezoidal Rule
14.3 Simpson's Rule Approximation for an Integral
14.4 Beyond Simpson's Rule
14.5 Romberg Integration
14.6 Gauss Quadrature
14.7 Improper Integrals
14.8 Double Integrals
14.9 Conclusion
Summary
Problems
H. Programming Assignment
H.1 Sample Program
□ Mechanical/Aeronautical Engineering: Shear Force on an Airplane Wing
H.2 Programming Problems
□ H-A: Nuclear Engineering: Shielding a Nuclear Reactor (Integration of Noisy Data)
□ H-B: Mechanical Engineering/Physics: Total Heat Radiation from a Hot Bar
□ H-C: Geology/Petroleum Engineering: Shape of the Earth, Curve Fitting with Legendre Polynomials
15. Numerical Solutions to Differential Equations
15.1 Introduction
15.2 Meaning of a Differential Equation
15.3 Computational Errors: A Question of Trade-Offs
15.4 Euler's Method
15.5 Improvements to Euler's Method
15.6 Method of Runge-Kutta
15.7 Predictor-Corrector Methods
15.8 Second-Order Differential Equations
15.9 Boundary-Value Problems
15.10 Conclusion
Summary
Problems
16. Error Analysis
16.1 Introduction
16.2 Review of Definitions Relating to Error Analysis
16.3 Types of Error
16.4 Round-Off Errors
16.5 Approximation Errors: Discretization and Truncation
16.6 Experimental Errors
16.7 Conclusion
Problems
Appendix: Summary of FORTRAN Statements and Grammar Rules
A.1 Procedure Statements
A.2 Specification Statements
A.3 Assignment and Program Control Statements
A.4 Flow-Control Statements
A.5 FORTRAN File-Directive Statements
A.6 Input/Output Statements
References
Answers and Solutions to Odd-Numbered Problems
Index
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