Link: Undergraduate Numerical Analysis/Methods Textbooks
Undergraduate Numerical Analysis/Methods Textbooks
Numerical Analysis
- Kendall E. Atkinson, An Introduction to Numerical Analysis (2nd ed.), John Wiley and Sons, 1989.
- Brian Bradie, A friendly introduction to Numerical Analysis , Pearson Prentice Hall, 2006.
- Burden and Faires, Numerical Analysis (8 ed), Brooks and Cole, 2005.
- Kincaid and Cheney, Numerical Analysis: Mathematics of Scientific Computation (3 ed), Brooks and Cole, 2002.
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.
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.
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.
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
These books are much more focused on developing the algorithms and tend to steer clear of any proofs or formalism. These books would be well suited for a non-math major numerical analysis course, or an applied numerical analysis course.- Kendall Atkinson and Weimin Han, Elementary Numerical Analysis (3 ed), John Wiley and Sons, 2004.
- 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.
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.
- Ayyub and McCuen, Numerical Methods for Engineers, Prentice Hall, 1996.
- Laurene Fausett, Applied Numerical Analysis using Matlab, Prentice Hall, 1999.
- Gerald and Wheatley, Applied Numerical Analysis (6 ed), Addison Wesley, 1997.
- Hager, Applied Numerical Linear Algebra, Prentice Hall, 1988.
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.
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.
- 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.
- Bell, Koren and Volinsky, Matrix factorization for recommender systems: www2.research.att.com/~vo
linsky/papers/ieeecompute r.pdf - Bell & Koren, Scalable Collaborative Filtering..: public.research.att.com/~
volinsky/netflix/BellKorI CDM07.pdf - Ilya Grigorik, SVD Recommendation System in Ruby: http://www.igvita.com/200
7/01/15... - Berry et al. Using linear algebra for intelligent information retrieval: http://www2.denizyuret.co
m/ref/b...
- Khan Academy, Linear Algebra: http://www.khanacademy.or
g/#line... - Stewart, The decompositional approach to matrix computation: http://galton.uchicago.ed
u/~lekh... - Halko, Martinsson and Tropp, Finding structure with randomness: http://amath.colorado.edu
/facult... - Press et al., Numerical Recipes: http://www.nr.com/
- Kempf, Numerical software tools in C: http://www.amazon.com/Num
erical-... - Dahlquist & Bjorck, Numerical Methods: http://www.amazon.com/Num
erical-... - Golub & Van Loan: Matrix Computations: http://www.amazon.com/Com
putatio... - Watkins, Fundamentals of Matrix Computations (this is a very gentle intro to the field): http://www.amazon.com/Fun
damenta... - Strang, Introduction to Applied Mathematics: http://www.amazon.com/Int
roducti... - Demmel, Applied Numeric Linear Algebra: http://www.amazon.com/App
lied-Nu... - Trefethen & Bau, Numerical linear algebra: http://www.amazon.com/Num
erical-... - Watkins: The Matrix Eigenvalue Problem: GR and Krylov Subspace
Methods: http://www.amazon.com/Matrix-Eig... - Parlett,The Symmetric Eigenvalue Problem: http://www.amazon.com/Sym
metric-... - Hildebrand, Introduction to Numerical Analysis: http://www.amazon.com/Int
roducti... - Iverson, Algebra: an algorithmic treatment: http://www.amazon.com/Alg
ebra-al... (online version, thanks to Devon Q. McCormick : http://booki.treehouse.su/algebr... ) - Lanczos, Linear Differential Operators: http://www.amazon.com/Dif
ferenti... - Bellman, Introduction to Matrix Analysis: http://www.amazon.com/Int
roducti... - Bertsekas, Parallel and Distributed Computation: Numerical
Methods:http://www.amazon.com/Parallel-D... - Hamming, Numerical Methods for Scientists and
Engineers: http://www.amazon.com/Numerical-... - Bierman, Factorization Methods for Discrete Sequential
Estimation: http://www.amazon.com/Factorizat... - Wilkinson, The algebraic Eigenvalue Problem: http://www.amazon.com/Alg
ebraic-... - Horn, Matrix Analysis: http://www.amazon.com/Mat
rix-Ana... - Courant & Hilbert, Methods of Mathematical Physics: http://www.amazon.com/Met
hods-Ma... - Harville, Matrix Algebra from a statistician perspective: http://www.amazon.com/gp/
product... - Fiedler, Special Matrices: http://www.amazon.com/Spe
cial-Ma... - Higham, Accuracy and stability of numerical algorithms: http://www.amazon.com/gp/
product... - Tewarson, Sparse Matrices: http://books.google.com/b
ooks?id... - Gill et al., Numerical linear algebra and optimization: http://books.google.com/b
ooks?id... - Gill et al., Practical Optimization: http://www.amazon.com/Pra
ctical-... - Langville & Meyer, Google Page Rank and Beyond: http://www.amazon.com/Goo
gles-Pa... - Godsil, Algebraic Graph Theory: http://www.amazon.com/Alg
ebraic-... - Nielsen, PageRank tutorial: http://michaelnielsen.org
/blog/u... - Mannix, Numerical recipes in Hadoop: http://www.slideshare.net
/jakema... - Vandebril et al., Matrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods: http://books.google.com/b
ooks?id... - Bickson, Matrix factorization algorithms: http://bickson.blogspot.c
om/2011... - Moler, Numerical Computing with MATLAB: http://www.mathworks.com/
moler/c... - Meurant, Computer solution of large linear systems: http://books.google.com/b
ooks?id... - Golub's works: http://www.amazon.com/s/r
ef=ntt_... - Dongarra's works: http://www.netlib.org/utk
/people... - Iverson, Algebra as a language: http://www.jsoftware.com/
papers/... - Petersen & Pedersen, The Matrix Cookbook: http://www.ics.uci.edu/~w
elling/... - Iserles, A First Course in the Numerical Analysis of Differential
Equations: http://www.amazon.com/Numerical-... - Morton & Mayers, Numerical Solution of Partial Differential Equations: http://www.amazon.com/Num
erical-... - Atkinson, Introduction to Numerical Analysis, on-line resources: ch1-5: http://www.cs.uiowa.edu/~
atkinso... , ch6-9: http://www.cs.uiowa.edu/~atkinso... - Mehta, Random Matrices: http://www.amazon.com/Ran
dom-Mat... - Fornasier, Theoretical Foundations and Numerical Methods for Sparse Recovery: http://www.amazon.com/gp/
product...
- Apache Mahout: https://cwiki.apache.org/
confluence/display/MAHOUT /Algorithms - http://numpy.scipy.org/
- http://www.sai.msu.su/sal
/B/1/ (thanks to Alex K. Chen for the link) - http://www.netlib.org/
- Junction trees in numerical analysis: http://yaroslavvb.blogspo
t.com/2... - GraphLab, A New Parallel Framework for Machine Learning: http://www.graphlab.ml.cm
u.edu/ - NAG C numerical library: http://www.nag.co.uk/nume
ric/CL/... - Dongarra et al., LINPACK user's guide: http://books.google.com/b
ooks/ab... - Burden & Faires, Numerical Analysis: http://books.google.nl/bo
oks/abo... - Simoncelli, Eero P. : A Geometric Review of Linear Algebra: Page on nyu.edu
- Jordan, M.I. An Introduction to Linear Algebra in Parallel Distributed Processing
4 comments:
Link: Transforming Numerical Methods Education for the STEM Undergraduate
Very good materials, lecture notes, slides, videos, exercises, all included!
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Link: EE364a: Convex Optimization I
A course from stanford, focusing on optimization.
Link: Linear Algebra and Multivariable Calculus
Some prerequisites.
Linear Algebra and Multivariable Calculus are two of the most widely used mathematical tools across all scientific disciplines. This course seeks to develop background in both and highlight the ways in which multivariable calculus can be naturally understood in terms of linear algebra.
This course assumes a strong understanding of differential calculus of one variable, as taught in the Math 41-42 series (or equivalent). For the linear algebra portion, we will start from the beginning and build up all concepts in lectures. However, this course is packed with information and moves very quickly. Students who are somewhat unsure of their mathematics background may want to consider courses in the 40 series. In particular, students missing the equivalent of Math 42 may find the portions of Math 51 that demand deeper conceptual understanding to be more difficult than those who have the experience of a full year of college-level calculus. (Students having quite a lot of experience with mathematical proof and who are looking for a more theoretical course may want to try Math 51H.)
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