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1897 results in Engineering mathematics and programming

Page 24 of 95

  • Preface

  • Jaan Kiusalaas, Pennsylvania State University
  • Book:
    Numerical Methods in Engineering with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    20 October 2015, pp ix-x

  • Summary

    This book is targeted primarily toward engineers and engineering students of advanced standing (sophomores, seniors, and graduate students). Familiarity with a computer language is required; knowledge of engineering mechanics (statics, dynamics, and mechanics of materials) is useful but not essential.

    The text places emphasis on numerical methods, not programming. Most engineers are not programmers but rather problem solvers. They want to know what methods can be applied to a given problem, their strengths and pitfalls, and how to implement them. Engineers are not expected to write computer code for basic tasks from scratch; they are more likely to utilize functions and subroutines that have already been written and tested. Thus programming by engineers is largely confined to assembling existing bits of code into a coherent package that solves the problem at hand.

    The “bit” of code is usually a function that implements a specific task. For the user, the details of the code are of secondary importance. What matters is the interface (what goes in and what comes out) and an understanding of the method on which the algorithm is based. Because no numerical algorithm is infallible, the importance of understanding the underlying method cannot be overemphasized; it is, in fact, the rationale behind learning numerical methods.

    This book attempts to conform to these views. Each numerical method is explained in detail, and its shortcomings are pointed out. The examples that follow individual topics fall into two categories: hand computations thatillustrate the inner workings of the method and small programs that show how the computer code is utilized in solving a problem. Problems that require programming are marked with ▄.

    The material consists of the usual topics covered in an engineering course on numerical methods: solution of equations, interpolation and data fitting, numerical differentiation and integration, solution of ordinary differential equations, and eigenvalue problems. The choice of methods within each topic is tilted toward relevance to engineering problems. For example, there is an extensive discussion of symmetric, sparsely populated coefficient matrices in the solution of simultaneous equations. In the same vein, the solution of eigenvalue problems concentrates on methods that efficiently extract specific eigenvalues from banded matrices.

    An important criterion used in the selection of methods was clarity. Algorithms requiring overly complex bookkeeping were rejected regardless of their efficiency and robustness.

  • 1 - Introduction to MATLAB

  • Jaan Kiusalaas, Pennsylvania State University
  • Book:
    Numerical Methods in Engineering with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    20 October 2015, pp 1-26

  • Summary

    Quick Overview

    This chapter is not intended to be a comprehensive manual of MATLAB®. Our sole aim is to provide sufficient information to give you a good start. If you are familiar with another computer language, and we assume that you are, it is not difficult to pick up the rest as you go.

    MATLAB is a high-level computer language for scientific computing and data visualization built around an interactive programming environment. It is becoming the premiere platform for scientific computing at educational institutions and research establishments. The great advantage of an interactive system is that programs can be tested and debugged quickly, allowing the user to concentrate more on the principles behind the program and less on programming itself. Because there is no need to compile, link, and execute after each correction, MATLAB programs can be developed in a much shorter time than equivalent FORTRAN or C programs. On the negative side, MATLAB does not produce stand-alone applications – the programs can be run only on computers that have MATLAB installed.

    MATLAB has other advantages over mainstream languages that contribute to rapid program development:

  • • MATLAB contains a large number of functions that access proven numerical libraries, such as LINPACK and EISPACK. This means that many common tasks (e.g., solution of simultaneous equations) can be accomplished with a single function call.

  • • Extensive graphics support allows the results of computations to be plotted with a few statements.

  • • All numerical objects are treated as double-precision arrays. Thus there is no need to declare data types and carry out type conversions.

  • • MATLAB programs are clean and easy to read; they lack the syntactic clutter of some mainstream languages (e.g., C).

    • The syntax of MATLAB resembles that of FORTRAN. To get an idea of the similarities between these programming languages, let us compare the codes written in the two languages for solution of simultaneous equations Ax = b by Gauss elimination (do not worry about understanding the inner workings of the programs).

Numerical Methods in Engineering with MATLAB®
  • 3rd edition
  • Jaan Kiusalaas
  • Published online:
    28 May 2018
    Print publication:
    20 October 2015
  • The third edition of this successful text describes and evaluates a range of widely used numerical methods, with an emphasis on problem solving. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB® M-files accompany each method and are available on the book's web page. Code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. The third edition features a new chapter on Euler's method, a number of new and improved examples and exercises, and programs which appear as function M-files. Numerical Methods in Engineering with MATLAB®, 3rd edition is a useful resource for both graduate students and practicing engineers.

  • Preface

  • Radhey S. Gupta, Indian Institute of Technology, Roorkee
  • Book:
    Elements of Numerical Analysis
    Published online:
    28 May 2018
    Print publication:
    14 May 2015, pp xv-xvi

  • Summary

    As I think of writing about the present work I am pleasantly reminded of a few names which occupy very special place in my academic and professional career. In 1966, while I was working at the Post Office Research Station in London (now most probably at Martlesham) I got introduced to computers. I cannot forget, with how much patience and perseverence, B.E. Surtees had not only helped but had almost taught me Algol programming. Later I used the computer extensively for solving scientific problems. Further, the Research Station generously granted me day-release to attend MSc (Comp.Sc.) course at the City University, London. Although I could not complete the course, I developed a strong liking for Numerical Analysis. It would be my privilege to mention the name of Professor V.E. Price who taught the subject with full devotion and dedication. I must admit that I learnt the basics of Numerical Analysis from there and much of it makes part of Chapters 1 to 7 and 10 of the book. I was greatly impressed by the book Modern Computing Methods by E.T. Goodwin, and still am. My intense desire for working in Numerical Analysis was fulfilled when I joined PhD in 1969 at Brunel University under the guidance of Professor J. Crank who was known internationally in the field. Luckily, a very challenging problem came my way to work upon from Hammersmith Hospital, London. The problem required knowledge for solving partial differential equations numerically. The first book on p.d.e., I read was G.D. Smith's who was coincidently teaching in the same department. Therefore no wonder, my treatment for solving p.d.e.'s in Chapter 11 may be biased towards his book. I worked with Professor Crank for five years – three years for my PhD and two years as a postdoctoral research fellow. It was only his constant inspiration that kept me going and galloping. Those five years, I may call the most precious years of my life. I came to know with deep sense of sorrow and grief that Professor Crank passed away in October 2006.

  • 16 - Free and Moving Boundary Problems: A Brief Introduction

  • Radhey S. Gupta, Indian Institute of Technology, Roorkee
  • Book:
    Elements of Numerical Analysis
    Published online:
    28 May 2018
    Print publication:
    14 May 2015, pp 709-722

  • Summary

    Introduction

    In Chapter 11, we have dealt with parabolic equations defined over certain domain D with some kind of conditions prescribed on the boundary S. In these problems the boundary remains fixed for all times. However, there are very many problems of great practical importance where the boundary does not remain stationary; it moves. The boundary (whole or part) changes its position, shape and/or size with time. That is, S becomes a function of time in addition to the space variables. Considering Cartesian coordinates, the boundary can move along the x-axis only in case of one-dimensional problem, in the x-y plane in case of two-dimensional problem and in space in the case of three-dimensional problem. These problems are called moving boundary problems (mbp's). The most common example of a mbp is found in heat flow when a solid undergoes melting or a liquid changes its state under the process of solidification. In the melting or solidification problems, the solid/liquid interface (moving boundary) separating the solid and the liquid phases is a function of space and time. Another example from heat flow may be that of ablation, i.e., removal of the material from the surface of a solid body due to excessive heating – a practical example may be that of ablation from the space capsule at the time of its re-entry into the earth's atmosphere. Other familiar examples may be like consolidation of earth dam or diffusion of a gas in an absorbing medium. Besides, many more examples of moving boundary problems may be found in reference [1].

    The free boundary problems (fbp's) are elliptic equations representing special type of steady state problems. They are defined over a fixed domain but location of the boundary is not known, a priori. A practical example of a fbp may be given from the context of ‘fluid flow through porous media’ is, the seepage of water into an earth dam.

Page 24 of 95