• Book Name: Introduction to Numerical and Analytical Methods with MATLAB
• Pages:544
• Size: 9 MB

# Introduction to Numerical and Analytical Methods with MATLAB

I have been teaching two courses in computer applications for engineers at Florida Atlantic University for many years. The first course is usually taken in the student’s sophomore year while the second course is usually taken in the student’s junior or senior year. Both computer classes are run as lecture-laboratory courses, and the MATLAB• software program is used in both courses. I have collaborated with several colleagues in writing two textbooks. The first was a textbook was titled Numerical and Analytical Methods with MATLAB•, with coauthors Drs. Chi-Tay Tsai and Oren Masory. This textbook was primarily oriented toward mechanical, civil, and aeronautical engineers. The second textbook was titled Numerical and Analytical Methods with MATLAB• for Electrical Engineers, with coauthor Dr. Andrew Stevens. This latest book is a composite of both textbooks and would be appropriate for all engineering students. The primary objectives of the textbook are to

1. Teach engineering students how to write computer programs (or scripts) on the MATLAB platform that solve engineering-type problems

2. Demonstrate various mathematical concepts that can be used to solve engineering- type problems, such as matrices, roots of equations, integration, ordinary differential equations, curve fitting, algebraic linear equations, and others

3. Demonstrate the use of numerical and analytical method for solving the mathematical problems associated with engineering-type problems, such as Simpson’s rule on integration, Gauss elimination method for solving a system of linear algebraic equations, the Runge–Kutta method for solving a system of ordinary differential equations, the iteration method for solving pipe flow problems, the Hardy Cross method for solving flow rates in a pipe network, the method of separation of variables to solve partial differential equations, the use of Laplace transforms to solve both ordinary and partial differential equations, and others.

## Introduction to Numerical and Analytical Methods with MATLAB

After receiving some feedback on the first textbook, I realized that for a first course in computer programming under the MATLAB platform, concepts in computer programming needed to be substantially expanded. This was undertaken in the second textbook as well as in this new textbook. The material covered in Chapter 2 of the second textbook is now covered in Chapters 2 and 3. Furthermore, I also decided not to cover topics that require additional MATLAB tool boxes, and as a result, I have eliminated the chapters on finite elements and controls. However, I did keep the chapter on optimization, which also requires an additional tool box.

The advantage of using the MATLAB software program over other software programs is that it contains built-in functions that numerically solve systems of linear equations, systems of ordinary differential equations, roots of transcendental equations, definite integrals, statistical problems, optimization problems, and many other types of problems encountered in engineering. A student version of the MATLAB program is available at a reasonable cost. However, to students, these built-in functions are essentially black boxes. By combining a textbook on MATLAB with basic numerical and analytical analysis (although I am sure that MATLAB uses more sophisticated numerical techniques than the ones that are described in this text), the mystery of what these black boxes might contain is somewhat alleviated. The text contains many sample MATLAB programs that should provide guidance to the student on completing the exercises and projects that are listed in each chapter. Projects are at the end of the chapters and are usually more difficult than the exercises. Many of the projects are nontrivial.

In recent times, I have used several exercise problems as in-class exams in which students submit their MATLAB programs and results to me on blackboard. Projects are given as take-home exams to be submitted to me within one or two weeks, depending on the difficulty of the project.

The advantage of running these courses (especially the first course) as a lecture laboratory course is that the instructor is in the computer laboratory to help the student debug his or her program. This includes the example programs as well as the exercises and the projects. Although this textbook is suitable for a first course in computer application for engineers, say at the sophomore level, there is enough material in the textbook that makes it suitable for a higher level course or as a reference book in higher level courses. All three textbooks contain many sample programs to teach the student programming techniques.

For a first course in computer applications, Chapters 1 through 6 would be appropriate. These chapters include review sections, which may be used by the course instructor to ask the class questions on the material that was recently covered. The topics covered in Chapters 1 through 6 are as follows: