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NUMERICAL METHODS WITH MATLAB® is intended as a resource or compendium of methods suitable for use in numerical methods and engineering problem-solving courses. This book details the main topics of numerical methods, such as linear analysis, analysis of functions of one or several variables, data analysis and modeling, and the solution of ordinary and partial differential equations. Borse emphasizes practical applications, while providing sufficient theory for students to understand the underlying operation, and strengths and weaknesses, of each technique. MATLAB® is used throughout; the text works equally well for students with or without prior background in MATLAB®. Students inexperienced in the use of MATLAB® can refer to the MATLAB® programming appendix at the back of the book, which introduces MATLAB® topics in the same sequence as they are presented in the numerical methods sections of the text. A computer disk containing a MATLAB® tutorial accompanies the text.

Dr. Garold (Gary) Joseph Borse (1940-2019) was born in Detroit, Michigan, and graduated from St. Rita's High School in 1958. Gary recei ved 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
Notes to the Instructor
Part I Linear Analysis and Matrices
Preview
Introduction
1. Fundamental Definitions
2. Solution of the Matrix Equation Ax=b
3. Matrix Eigenvalue Equations
Bibliography for Part I
Part II MATLAB Applied to Functions of a Single Variable
Preview
Introduction
4. Series Expansions for Functions
5. Roots of Functions of a Single Variable
6. Minimum or Maximum of a Function
7. Numerical Integration Techniques
Bibliography of Part II
Part III Functions of Two or More Variables
Preview
Introduction
8. Derivatives of Multivariable Functions
9. Roots of Multivariable Functions
10. Minimization of a Multivariable Function
11. Multiple Integrals
12. Monte Carlo Integration
Bibliography of Part III
Part IV Data Analysis and Modeling
Preview
13. Statistical Description of Data
14. Linear Least Squares Analysis
15. Nonlinear Least Squares
16. Interpolation and Spline Fits
17. Fourier Analysis
Bibliography of Part IV
Part V Differential Equations
Preview
18. Elementary Concepts
19. Initial Value Differential Equations
20. Two-Point Boundary Value Problems
21. The Method of Superposition
22. Introduction to Partial Differential Equations
Bibliography of Part V
Appendix Programming in MATLAB
A.i Matrix Algebra in MATLAB
A.ii Polynomials and Other Functions
A.iii MATLAB Logical Structures
A.iv Two-Dimensional Plotting
A.v Constructing and Plotting Multivariable Functions
A.vi Elementary Input/Output in MATLAB
Answers
Index
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