This text is for courses in numerical methods offered in departments of civil or mechanical engineering and departments of mathematics. Its objective is to introduce the engineer and scientist to numerical methods used to solve mathematical problems that cannot be solved by exact methods. With the general accessibility of highspeed digital computers, it is now possible to obtain rapid and accurate solutions. Mastery of the material presented in this book will prepare engineers and scientists to solve many of their everyday problems, give them insight to recognize when other methods are required, and give them the necessary background to study additional methods. Part I discusses the Basic Tools of Numerical Analysis and considers many of the basic problems that arise in all branches of engineering and science. Part II is devoted to the numerical solution of ordinary differential equations (ODEs). Part III covers the numerical solution of partial differential equations (PDEs). The approach taken is to introduce a type of problem, present sufficient background to understand the problem and possible methods of solution, develop one or more numerical methods for solving the problem, and illustrate the numerical methods with examples. In most cases, the numerical methods presented to solve a particular problem proceed from simple methods to complex methods.
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5.0 out of 5 stars
Perfect numerical methods book as one can get for a 1st course.,
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This review is from: Numerical Methods for Engineers and Scientists, Second Edition, (Hardcover)
A great textbook for a first course in Numerical Methods as it gives an extensive yet detailed coverage of numerical techniques that form the base for more advanced work in CFD. This book is based almost entirely on the finite difference method for solving differential equations. A chapter addresses finite element techniques but it only a primer; you will need a textbook solely devoted to FEM. This book is written for a mechanical engineer, as most of the governing equations are invariably from the areas of heat transfer, fluid flow, gas dynamics and solid mechanics.
The good points are 1. Each method described comes with a index notated formula that takes the head ache out of programming. Plus there are plenty of FORTRAN subroutines to look at. 2. Not only does Hoffman give you the finite difference equation he also throws in a solved example with one or two iterations worked out in full detail; the benefit of this cannot be overstated. 3. Plenty of practice problems with results at the back of the book. 4. Enough math to give the reader an insight into how the method works. If you care for rigor this is not the book. The drawbacks are 1. Hoffman has condensed the portions dealing with PDE's from previous editions cutting out some theoretical development. Since most wouldn't have had a course in PDE's (like me) a few more pages might have better squared away a few difficult concepts (eg. characteristic lines of PDE's). 2. Could use another round of proof-reading. This book is littered with typos; which one runs into even in key formulas. This is unacceptable in what is otherwise a pedagogically sound book. 3. I would have liked to see some more elaboration on multidimensional problems in PDE's apart from the 1D unsteady examples which form the workhorse. Hoffman mentions that the explicit methods for 1D unsteady problems work for higher while the implicit schemes introduce numerical complexity which merit advanced methods. These specialized methods for higher dimensional parabolic and hyperbolic PDE's are not developed. As it stands the book is packed with enough material for 3 semesters study. This book works well for self study. Everything from linear algebra (direct and iterative methods, LU factorization, eigenproblems), non-linear eqns, interpolation, numerical integration and differentiation, ODE's, BVP's, and PDE's is touched upon. Unlike most introductory texts Hoffman doesn't shy away from non-linear problems in differential equations. I used it for the num. methods course even though the prescribed text was Heath's Scientific Computing which was the worst textbook I ever read (thankfully never purchased it). If you are getting started in CFD then this book provides a solid first step.
4.0 out of 5 stars
Great Book,
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This review is from: Numerical Methods for Engineers and Scientists, Second Edition, (Hardcover)
This book is great an explaining principle, providing examples, and sample code. It would be improved my more visual explanation of method procedures.
5.0 out of 5 stars
Good Book To start, Finite Element Methods,
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This review is from: Numerical Methods for Engineers and Scientists, Second Edition, (Hardcover)
I spend couple of months on searching a good book on Numerical method specifically a introductory text on Finite Element Methods
and finally found this one. This is a good book for any one who do not have any experience of Finite Element Methods before. To understand Finite Element Methods, it would be help full if one flows along the progression of the book rather then reading specific chapters. Overall, This is a good book for Numerical Method and best Introduction to Finite element Methods I have read so far.
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First Sentence:
This Introduction contains a brief description of the objectives, approach, and organization of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
modified midpoint method, direct fit polynomials, program main defines, data ndim, derivative function evaluations, exact partial derivatives, remainder term yields, information propagation speed, direct power method, global solution domain, interpolating polynominals, leading truncation error terms, shifted power method, results output flag, asymptotic steady state solution, fitting approximating polynomials, linear convection equation, algebraic finite difference equation, more prominent packages, real characteristic paths, shifted inverse power method, subroutine lufactor, diffusion equation solver, heat diffusion problem, least squares straight line approximation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Work Problem, Summary Problems Examples, Numerical Recipes, Dividing Eqs, Repeat Problem, Summary Four, Use Gauss-Jordan, Work Example New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This Introduction contains a brief description of the objectives, approach, and organization of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
modified midpoint method, direct fit polynomials, program main defines, data ndim, derivative function evaluations, exact partial derivatives, remainder term yields, information propagation speed, direct power method, global solution domain, interpolating polynominals, leading truncation error terms, shifted power method, results output flag, asymptotic steady state solution, fitting approximating polynomials, linear convection equation, algebraic finite difference equation, more prominent packages, real characteristic paths, shifted inverse power method, subroutine lufactor, diffusion equation solver, heat diffusion problem, least squares straight line approximation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Work Problem, Summary Problems Examples, Numerical Recipes, Dividing Eqs, Repeat Problem, Summary Four, Use Gauss-Jordan, Work Example New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 24
books:
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27
books
cite this book:
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- Numerical Recipes: The Art of Scientific Computing by William H. Press on 8 pages
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter (1), and Back Matter (2)
- Introduction to Fluid Mechanics by Robert W. Fox in Back Matter
- Introduction to Fluid Mechanics by James E. A. John in Back Matter
- Gas Dynamics by Maurice J. Zucrow in Back Matter
See all 24 books this book cites
- Introduction to Theoretical and Computational Fluid Dynamics by C. Pozrikidis on page 598, and page 630
- ANALYTICAL and NUMERICAL METHODS WITH THE HP 48 G/G+/GX PROGRAMMABLE CALCULATOR by Gilberto Urroz on page 1, and page 58
- Numerical Computation in Science and Engineering by C. Pozrikidis on page 580
- Introduction to Structural Dynamics (Cambridge Aerospace Series) by Bruce K. Donaldson on page 480
- Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Antennas and Propagation Library) by Susan C. Hagness on page 64
See all 27 books citing this book
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