Numerical Analysis

• Kendall E. Atkinson, An Introduction to Numerical Analysis (2nd ed.), John Wiley and Sons, 1989.

Probably the most formal undergraduate numerical analysis text around.  Has all the standard topics:  root finding, interpolation, numerical integration, solving ODEs, solving linear systems, and the matrix eigenvalue problem.  This is a good textbook, but very formal.
 
• Brian Bradie, A friendly introduction to Numerical Analysis , Pearson Prentice Hall, 2006.

A new book on the scene that makes a nice addition to the traditional favorites. One of the provided resources is a website stocked with programs in C and Matlab. The topics include some of the classic coverage of interpolation and root finding, but this book also has expanded coverage on differential equations and a very nice coverage on solving PDEs.  
 
• Burden and Faires, Numerical Analysis (8 ed), Brooks and Cole, 2005.

A very popular text for undergraduate numerical analysis.  This book is not as formal as Atkinson and students have an easy time reading through the chapters.  The book is very large and covers a large range of the classic topics:    root finding, interpolation, numerical integration, solving ODEs, solving linear systems, solving nonlinear systems, the matrix eigenvalue problem, boundary value problems, and a brief introduction to solving PDEs.
 
• Kincaid and Cheney, Numerical Analysis: Mathematics of Scientific Computation (3 ed), Brooks and Cole, 2002.

This book is very similar to Burden and Faires.  This is another large book with a long list of topics: root finding, interpolation, numerical integration, solving ODEs, solving linear systems, solving nonlinear systems, numerical linear algebra, boundary value problems, an introduction to linear programming, and a brief introduction to solving PDEs.  The differences between the Burden book and the Kincaid book really boil down to the examples and the exercises.

Numerical Methods

• Kendall Atkinson and Weimin Han, Elementary Numerical Analysis (3 ed), John Wiley and Sons, 2004.

The authors do a good job of taking very formal material and shooting for a much lower level.  This still very much a math centered book and not very application oriented.  Topics include:  error propagation, root finding, interpolation, numerical integration, solutions of linear systems, solutions to ODEs, numerical linear algebra, and finite difference methods for PDEs.
 
• Steven Chapra Applied Numerical Methods with Matlab (for Engineers and Scientists), McGraw-Hill, 2005. Three things to note: Fairly extensive use of curve fitting; could use a CD or a website to provide Matlab files to the less proficient programs; and bungee jumping on the cover of a numerical methods book?

 
• James F. Epperson, An introduction to Numerical Methods and Analysis, Wiley & Sons, 2002.
  This book is a nice attempt to link the analysis that is needed in numerical analysis with the utility that is desired in a numerical methods class. Review of the prerequisite mathematical theory is covered in the first chapter and proofs for some of the major theorems is gathered in the appendix. The flow of the book is very much a feel of numerical methods, but the nuggets of analysis can be found in strategic locations.
   
• Cheney and Kincaid Numerical Mathematics and Computing (5 ed), Brooks/Cole, 2004.

• Ayyub and McCuen, Numerical Methods for Engineers, Prentice Hall, 1996.

Good textbook.  Almost enough theory to be used for a numerical analysis text (but not enough), however there is plenty of material for an applied numerical analysis book.  You might not use this book, but you will not regret reviewing a copy.  Topics include:  root finding, a very nice solving linear systems chapter, interpolation, numerical integration, a nice solving ODEs chapter, regression analysis, and an interesting data description and treatment chapter.  Great reference book.
 
• Laurene Fausett, Applied Numerical Analysis using Matlab, Prentice Hall, 1999.

 
• Gerald and Wheatley, Applied Numerical Analysis (6 ed), Addison Wesley, 1997.

The long standing classic of this particular type of textbook.  The book is well written and offers a few good  applications and examples.  This book features large at the end problem sets with a wide variety of exercises.  Topics include:  Solving nonlinear systems, solving linear systems, interpolation, numerical integration, solving odes, boundary value problems, solving PDEs, and a Finite Element method chapter.
 
• Hager, Applied Numerical Linear Algebra, Prentice Hall, 1988.

• Lindfield and Penny, Numerical Methods using Matlab (2 ed), Prentice Hall, 2000.

• John H. Mathews and Kurtis D. Fink, Numerical Methods Using Matlab (3 ed), by J, Prentice Hall.

The contents in this book enable students to use sophisticated software insightfully and critically, with a basic understanding of the algorithms employed by the software, their strengths, weaknesses, and pitfalls. Emphasis is more on computations and less on theoretical analysis.

• Parviz Moin. Fundamentals of Engineering Numerical Analysis, Cambridge University Press, 2001.

Very succinct text, but also small and affordable paper back. The target audience appears to be students interested in advanced numerical methods. The text also has the unique feature of a discrete transform chapter and a hefty chapter on numerical methods for partial differential equations.

• Cleve Moler. Numerical Computing with Matlab, SIAM, 2004.

Learn Matlab from the person that started Matlab. The book does focus on how to use Matlab and shows the master at work with great illustrations of Matlab's muscle. Not a great source for teaching an undergraduate class, but it does make a great reference or optional text.

• Robert Schilling and Sandra Harris. Applied Numerical Methods for Engineers (Using Matlab and C), Brooks / Cole 2000.

This book is a wealth of material with standard content of root finding, differentiation, integration, ordinary differential equations, partial differential equations, and, linear systems, etc. However, there are additional topics that are not standard: Digital Signal Processing, optimization, and a healthy discussion of C libraries and Matlab.

• Charles Van Loan, Introduction to Scientific Computing (A matrix-vector approach using Matlab) (2 ed), Prentice Hall, 2000.