WILLIAM PATERSON UNIVERSITY OF NEW JERSEY 
COLLEGE OF SCIENCE AND HEALTH 
Computer Science Syllabus and Outline  

1. Course: CS402-01   Numerical Methods,  3 credits 
2. Department secretary:  Carol Parken (Science Hall East 5021) can be contacted
by telephone at (973)_720-2649  and  by e-mail at  ParkenC@wpunj.edu
3. Semester offered:  Spring 2013      
Time:  Tuesday & Thursday   3:30PM - 4:45PM            Location: Science Hall East 5019  
4. Faculty:  Dr.  John Najarian,  Prof. of Computer Science 
Office: Science Hall East 5032,  Phone: (973)-720-3383,  E-mail:   NajarianJ@wpunj.edu
Office Hours:     Tuesday and Thursday  2:00PM - 3:15PM
                            and also other hours can be arranged by appointment.
5. Required Texts (4): 

1. Timothy Sauer. "Numerical Analysis".  
    2nd ed. Pearson. 2012. 
    ISBN-10: 0321783670,        
    ISBN-13:  9780321783677  
    (The Primary Textbook)

http://www.pearsonhighered.com/educator/
product/Numerical-Analysis/9780321783677.page

Sauer's Source code (MATLAB)
http://wps.aw.com/aw_sauer_numerical_2/  


2. Moler, Cleve. "Numerical Computing with MATLAB".    
    SIAM, 2004.  Online version (free) at:
    http://www.mathworks.com/moler/chapters.html
    (To learn and program in MATLAB)


3.  Scheid, Francis. "Schaum's Outline of  Numerical Analysis". Online version (free) at:
     http://archive.org/details/SchaumsTheoryProblemsOfNumericalAnalysis     (PDF with text)
     (Best workbook in the area)    


4. We will occasionally use Greenbaum's notes cited below.   They are magnificent.  

If additional tutorial/facilitation is needed, visit the CS tutors for more texts and help as well as the library;  consider Fogiel[1983] REA workbook, Gerald & Wheatley, Burden, Hamming's classics, or other texts in the library or tutoring center.  Join our fine study groups.


Suggested Readings (not required):

Joe D. Hoffman and  Steven Frankel.  "Numerical Methods for Engineers and Scientists", Third
Edition, CRC Press,  2013.  (publication too late for this semester)


Anne Greenbaum and Timothy P. Chartier .  "Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms".  Princeton, 2012.     (exciting, modern, diverse app's, & challenging )  
(sites:   http://press.princeton.edu/titles/9763.html ,
              http://www.davidson.edu/math/chartier/numerical/,
              http://www.math.washington.edu/~greenbau/Math_464/
              http://www.math.washington.edu/~greenbau/Math_498/,
              http://www.math.washington.edu/~greenbau/Short_Course_in_Hanoi/Course_Notes/page.html).

Roger A. Horn and  Charles R. Johnson. "
"Matrix Analysis". 2nd ed. Cambridge University Press, 2012.
(comprehensive reference)

Ronald W. Larsen.  "Engineering with Excel", 4th ed. Prentice Hall, 2012.  (Excel proto-typing; slow but fun)  

Eric Lengyel.  "Mathematics for 3D Game Programming and Computer Graphics", Third Edition,
Cengage, 2011.    (Chapters 1,2,3,4,7,11,13-16, and Appendix D all apply or cover most numerical methods.)
              http://www.mathfor3dgameprogramming.com/

Amos Gilat and Vish Subramaniam. "Numerical Methods with MATLAB". 2nd Edition,  Wiley, 2010.
(engineering perspective, popular)    

David S. Watkins. "Fundamentals of Matrix Computations". Wiley. 2010.

Steven C. Chapra. “Applied Numerical Methods with MATLAB for Engineers and Scientists”, Sixth Edition,
McGraw Hill, 2008.   (the Non-Applied book on the line below is superior).


Steven C. Chapra. “Numerical Methods for Engineers”, Sixth Edition, McGraw Hill, 2008.

Germund Dahlquist and Ake Bjorck.  "Numerical Methods in Scientific Computing, Volume I", SIAM, 2008
(graduate level; support material at:   http://www.siam.org/books/ot103/ ).  

Yang X. S. "Introduction to Computational Mathematics", World Scientific Publishing
, 2008.

James F. Epperson, "An Introduction to Numerical Methods and Analysis", Revised Edition, Wiley 2007.

M.K. Jain, S. Iyengar, and R.K. Jain. "Numerical Methods for Scientific and Engineering Computation".
5th ed.  
New Age International Pvt Ltd Publishers, 2007.

Steven C. Chapra and Raymond Canale. “Numerical Methods for Engineers”. 5th ed. McGraw Hill, 2006.

Brian Bradie, “Friendly Introduction to Numerical Analysis, A”,  Prentice Hall, 2006.    

Richard Burden and J.J. Faires.   “Numerical Analysis”. Eighth Edition,  Brooks/Cole, 2005. 

Jeffery J. Leader,   “Numerical Analysis and Scientific Computation”, Addison-Wesley,  2005.

Kendall Atkinson and Weimin Han.  "Elementary Numerical Analysis", 3rd Edition, Wiley, 2004.

Gerald Curtis & Patrick Wheatley, “Applied Numerical Analysis”,  Seventh Edition,  Addison and Wesley, 2004.

Moler, Cleve.  "Numerical Computing with MATLAB",    SIAM, 2004.  Online version (free) at:
http://www.mathworks.com/moler/chapters.html

Ward Cheney and David Kincaid. “Numerical Mathematics and Computing”, Fifth  Edition, Brooks/Cole Publishing Company, 2004.

Alan Law,   “Introduction to Scientific Computing Using MATLAB”, Prentice Hall, 2004.

Christopher J. Zarowski,  "An Introduction to Numerical Analysis for Electrical and Computer Engineers"
Wiley,  2004.

J. Douglas Faires and Richard Burden, “Numerical Methods”, Third Edition, Brooks/Cole, 2003.   

Recktenwald, Gerald. " Numerical Methods with MATLAB:Implementations and Applications",
Prentice Hall 2003.

Michael T. Heath,  “Scientific Computing”, Second Edition, McGraw Hill, 2002.
http://www.cse.uiuc.edu/heath/scicomp/
   (just wonderful, a must read)    

Singiresu S. Rao,    “Applied Numerical Methods for Engineers and Scientists”, Prentice Hall, 2002.  

Katsman, J.J. "Numerical Methods". Tomsk: TPU Press, 2002.  
ftp://ftp.ce.cctpu.edu.ru/study/Katsman/public/Apply_math/     (Book.doc and Num_met_workbook.doc)

Joe D. Hoffman and  Steven Frankel.  "Numerical Methods for Engineers and Scientists", Second
Edition, CRC Press,  2001.    (a classic textbook)

Meyer, Carl.   "Matrix Analysis and Applied Linear Algebra Book" (and  its" Solutions Manual".
SIAM, 2001.   (great textbook for foundations)  http://matrixanalysis.com/DownloadChapters.html    
Also visit:  http://meyer.math.ncsu.edu/, his site.       

Laurene V. Fausett,   “Applied Numerical Analysis Using MATLAB”,  Prentice Hall, 1999. 

L.F. Shampine , R.C. Allen and S. Pruess,  “Fundamentals of Numerical Computing”, Wiley, 1997.

James W. Demmel. "
Applied Numerical Linear Algebra", SIAM, 1997.  http://www.cs.berkeley.edu/~demmel/

Lloyd N. Trefethen and David Bau III.   "
Numerical Linear Algebra ", SIAM, 1997.

G. H. Golub and Van Loan, C , "Matrix Computations", Johns Hopkins Press,  1996.

GM Phillips and PJ Taylor,  “Theory and Applications of Numerical Analysis”,  Academic Press, 1996.  

G.W. "Afternotes on Numerical Analysis", SIAM, 1996.  

N. S. Asaithambi, “Numerical Analysis, Theory and Practice”, Saunders College Publishing, 1995.  

Roger A. Horn and  Charles R. Johnson.   "
Topics in Matrix Analysis ",  Cambridge University Press, 1994.

Terrence J. Akai,    “Applied Numerical Methods for Engineers”, Wiley, 1994.

Shoichiro Nakamura ,  “Applied Numerical Analysis in C”, Prentice Hall, 1993.

Atkinson, 
Kendall E. "An Introduction to Numerical Analysis", Wiley, 1989. (distinct from Atkinson[2004])

Francis Scheid.  "Schaum's Outline of Numerical Analysis". 2nd ed. McGraw-Hill, 1989.

Sidney Yakowitz and Ferenc Szidarovszky. "Introduction to Numerical Computations", 2nd ed.
Prentice Hall, 1989.

Paul Hultquist,   "Numerical Methods for Engineers and Computer Scientist”, Addison-Wesley,  1988. 

R. W. Hamming,   Numerical Methods for Scientists and Engineers,  Dover Reprint, 1987.  (a classic)

M.J. Maron,   “Numerical Analysis”, Second Edition, Macmilian, 1987.

M. Fogiel.  "
Numerical Analysis Problem Solver".  Research Education Associates (REA), 1983.   

Anthony Ralston and Philip Rabinowitz.   "A First Course in Numerical Analysis". Second Edition,
McGraw Hill, 1978 (Dover Reprint, 2001).    (classic)  

B. Noble and J. Daniel,     “Applied Linear Algebra”, Prentice Hall, 1977.  

Germund Dahlquist and Ake Bjorck.  "Numerical Methods", Prentice-Hall, 1974  (Dover reprint, 2003).   

S. D. Conte, and Carl de Boor,     “Elementary Numerical Analysis: An Algorithmic Approach”, Second Edition, McGraw Hill, 1972.  

Eugene Isaacson and Herbert Keller,     “Analysis of Numerical Methods”, John Wiley, 1966.

Kaiser Kunz,     “Numerical Analysis”, McGraw Hill, 1957. 

F. B. Hildebrand,    “Introduction to Numerical Analysis”, McGraw Hill, 1956 (Dover Reprint 2nd ed, 1987). 



Recommended Academic Numerical Methods Websites
:                      

   http://www.math.washington.edu/~greenbau/     Outstanding notes on every 400-level course.

   http://www.cse.uiuc.edu/heath/scicomp/   Heath's Scientific Computing (excellent)    

   http://www.math.nyu.edu/faculty/goodman/teaching/Scientific_Computing/scientific_computing.html
   (fine set of notes on Scientific Computing) 

    Moler, Cleve.  "Numerical Computing with MATLAB",  SIAM, 2004.  Online version (free)
    at:    http://www.mathworks.com/moler/chapters.html

   http://en.wikipedia.org/wiki/Numerical_analysis   The Ubiquitous Wikipedia's corner  

   Of the next four links, the first most closely matches our syllabus, then the second, third...
   http://ocw.mit.edu/courses/mechanical-engineering/2-993j-introduction-to-numerical-analysis-for-engineering-13-002j-spring-2005/
    http://ocw.mit.edu/courses/mechanical-engineering/2-086-numerical-computation-for-mechanical-engineers-spring-2012/    
    
http://ocw.mit.edu/courses/mathematics/18-335j-introduction-to-numerical-methods-fall-2010/      
   http://ocw.mit.edu/courses/mathematics/18-335j-introduction-to-numerical-methods-fall-2004/    
   Click here for the later topics in the textbook:  Partial Differential Equations,  Optimization
   http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm
   Some preliminary material from Strang is at:  http://math.mit.edu/linearalgebra/  (Tops in LA)  
   Some material is available at:  Sci-Prog-2011.         


   http://my.fit.edu/~jim/classes/      Useful problem-sets in several numerical methods courses.
   Use both the Heath (Fall'05 semester) and Greenbaum (Fall'07 semester) models.

   http://matrixanalysis.com/DownloadChapters.html      Meyer's Matrix Analysis (magnificent)
   http://meyer.math.ncsu.edu/     Course material on Meyer's foundations. 
   http://meyer.math.ncsu.edu/Meyer/Talks/Talks_Index.html   Research esp. Google Rank ...
   
   http://www.netlib.org/templates/templates.pdf   Templates to solve of linear systems, 2nd_ed.
   Iterative methods are illustrated in synoptic templates and constrasted in a concise manner.  

   http://web.eecs.utk.edu/~dongarra/etemplates/index.html  Templates for eigenvalue algorithms.

   http://dpl.ceegs.ohio-state.edu/courses/CV406/2012spring/  Applied to civil engineering,
   good motivating slides and contextual perspective.   

   http://www.eecs.berkeley.edu/~wkahan/Math128/     Excellent articles on Numerical Analysis

   http://www.cs.berkeley.edu/~demmel/ma221_Fall10/   Dummel's Num. Lin Algebra  
   
   http://www.eecs.berkeley.edu/~wkahan/MathH110/index.html   Excellent articles on LA.

   http://www.cs.cmu.edu/~jrs/jrspapers.html#cg  Painless Conjugate Gradient paper
   (also nice triangulation and mesh papers for Computer Graphics)      

   http://en.wikipedia.org/wiki/IEEE_754-2008       Floating Point

   http://www1.maths.leeds.ac.uk/~kersale/2600/       Numerical Analysis at Leeds (concise)
   http://www1.maths.leeds.ac.uk/~kersale/teaching.html  Branching to PDE's (good synopsis)   
   http://www.ece.mcmaster.ca/~reilly/3sk4_01/outline.htm   CAE perspective on Num. Meth.
   http://www.ece.mcmaster.ca/~kiruba/3sk3/3sk3.html         
   http://maecourses.ucsd.edu/~smicheli/mae107-s209      
   http://www.public.asu.edu/~hhuang38/MAE384.html       (Num. Meth. for Engineering)
   http://www.as.ysu.edu/~faires/Numerical-Analysis/Programs/  Burden & Faires (9th ed) code


MATLAB References, Tutorials ...
   
   http://www.mathworks.com/moler/chapters.html    (Best book by MATLAB's creator)
   Moler, Cleve. "Numerical Computing with MATLAB",  SIAM, 2004.

   http://www.mathworks.com/academia/  has numerous tutorials on  MATLAB and its
   many toolboxes.   The site has a bountiful cornucopia of links for further inquiry & learning.   
   http://www.mathworks.com/academia/student_version/start.html    12 Introductory Videos       

   http://www.cs.berkeley.edu/~clancy/sp.study.guides/9A.sg.pdf      MATLAB Study Guide
   http://www.math.ucsd.edu/~bdriver/21d-s99/matlab-primer.html    Fine Primer

   http://www.math.mtu.edu/~msgocken/intro/intro.html    

   http://www2.math.uic.edu/~hanson/MATLABhelp.html      

   http://www.che.utah.edu/~sutherland/wiki/index.php/Main_Page    Great MATLAB Wiki
           
   http://www.indiana.edu/~statmath/math/matlab/         (several tutorials)
   http://www.indiana.edu/~statmath/math/matlab/gettingstarted/printable.pdf   



Resources for Development (when we are not using C++ or general programming IDE's)

   Numerical Methods packages and libraries with development environments which we will use
   include (sorted by degree of use and expected preference): 
   1. MATLAB (in our labs), used in science and engineering industries, the commercial package 
       with powerful/fast routines, graphics, and toolboxes  (http://www.mathworks.com).              
   2. Microsoft Excel for rapid proto-typing. 
   3. FREEMAT (free, like MATLAB), downloadable from  http://freemat.sourceforge.net/
   4. Maxima (free Macsyma variant, the great original;  http://maxima.sourceforge.net/ ),  
   5. GNU Octave (like MATLAB also) download from  http://www.gnu.org/software/octave/,  
   6. SciLab (Scientific Software Package - open source)    http://www.scilab.org/        
       Download from:   http://www.scilab.org/products/scilab/download.  
       Tutorials at:          http://hkumath.hku.hk/~nkt/Scilab/IntroToScilab.html and     
       http://www-irma.u-strasbg.fr/~sonnen/SCILAB_HELP/scilab_for_dummies.htm.             
   0.  The great treasure trove of public domain numerical algorithms is  http://www.netlib.org/.

   Classic libraries include IMSL and NAG; specialized ones are LA-, QUAD-, & EIS-PACK.

   Popular alternatives to MATLAB you will encounter elsewhere are Mathematica
   (in the Math lab, strong on symbolic processing, graphics, multi-lingual programmabilty,
   with the enriching heritage of the Wolfram style and phlosophy :), MathCAD, and Maple.    
   For further reference on other numerical methods software, consult:            
         http://en.wikipedia.org/wiki/List_of_numerical_libraries
         http://en.wikipedia.org/wiki/Comparison_of_numerical_analysis_software    
         http://en.wikipedia.org/wiki/List_of_numerical_analysis_software
         http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems   
         http://en.wikipedia.org/wiki/List_of_computer_algebra_systems
         http://en.wikipedia.org/wiki/List_of_graphing_software

    For ODE solving, we will contrast with:
       http://www.math.uiuc.edu/iode/,  http://www.jens-langner.de/dessolver/,   
       http://www2.seminolestate.edu/lvosbury/DiffEq_Folder/DiffEq.htm,        .
    Try out:    http://www.berkeleymadonna.com/. Also read: http://www.jirka.org/diffyqs/.
    Lastly, visit: http://www.synechism.org/wp/difference-equations-to-differential-equations/  


Support Tools (for Lab and Home):   (Free Visual Compilers for Windows (dot.Net))    

Microsoft Visual Studio (including Visual C++) version 6 upto (dot.Net, 2010)
are available for FREE to all students taking CS courses at WPUNJ.  
Just fill out form when distributed in class or go to:
      http://cs.wpunj.edu/cs/MS_Alliance.html 
MS will provide disk images to burn the full Visual Studio dot.Net / 2010 Professional.
Also available are several other MS software packages including Windows XP, Vista,
Windows 7, Virtual PC ...  for student owned PC's.

Visual Studio 2008, 2010, & 2012RC  Express Editions (has MS Visual C/C++)
(For general public free versions of Microsoft Visual C/C++, just click "Downloads" or DVD)

Helpful Visual C++ sites are:   

Microsoft Visual C++.NET Tutorial
        http://cs.wpunj.edu/cs/labs/Microsoft_Visual_C++.NET_Tutorial.pdf    

Microsoft Visual C++ 6.0 Tutorial
        http://cs.wpunj.edu/cs/labs/Microsoft_Visual_C++_6.0_Tutorial.pdf

http://en.wikipedia.org/wiki/Microsoft_Visual_Studio   (Wikipedia, the free encyclopedia)

Microsoft's own Visual Studio 2010 C++ Tutorials, Prog. Guide, & Ref.   (indexed forward)


More Compilers and IDE's for C++:  (Free C++ Compilers (Need IDE to implement ideas :))    

Dev-C++: Free Windows C/C++ IDE & compiler at http://www.bloodshed.net/download.htm
You can put  Dev-C++ on a flash drive and be sleekly portable, "have compiler, will travel" 
(i.e. no registry entanglements or commitments :)  

Eclipse C/C++ Development Tooling  IDE and compiler

Open Watcom - Most Robust Compiler and Tools (free)     http://www.openwatcom.org/

6. Course Objectives: 
  1.  To learn topics in basis numerical analysis and methods used to solve physical problems
  2. To hone students’ programming skill using appropriate programming language(s)
  3. To further develop concepts and theories in analysis and construct of algorithms
  4. To sharpen students’ problem solving techniques as well as their analytical and intellectual thought processes

Course Description:

An introduction course in numerical methods, theory and application.  Emphasizes building algorithms for solution of numerical problems, the sensitivity of these algorithms to numerical errors and efficiency of these algorithm.  Topics include: solutions to non-linear equations; system of linear equations, interpolation, polynomial approximations, and quadrature  solutions; numerical differentiations and integrations, eigenvalues and eigenvectors.

Besides hand-computation, we will be programming in C++/Java, MATLAB, and several other packages (cited above) as well as prototyping in Excel.  

7. Student learning outcomes:  

Upon completion of the course, students will be able to:

1.      Acquire basic knowledge in theory and application of numerical methods used to solve physical problems. Measure: exams, surveys, and projects.

2.      Gain advanced programming skills in the appropriate programming language(s). Measure: exams and projects.

3.      Enhance their ability in analysis and construct of algorithms related to numerical  methods.  Measure: exams and projects.

4.      Improve analytical and intellectual thought process in problem solving. Measure: exams and projects.

5.      Strengthen their ability to present material both in oral and written form via homework and project participation.  Measure: exams, homework and projects.

6.      Enhance problem solving skills        Measure: exams, homework and projects.        

8. Topical Outline of the course content (tentatively each week = 1 chapter):

-1.  Introduction
   Review Syllabus, Algebraic Review, Floating Point & IEE standards, Errors, & Notation.
   Disasters in seemingly trivial computation:
   Case study #1   "Computers cannot store numbers."  
        Decimal 0.1 has no binary computer representation 
   Case study #2   "Infinite errors occur in simple sums."  
        Harmonic series (Sigma 1/k) is infinite, yet all computer sums "converge" to a finite answer.  
   Case study #3   "Even tiny errors cause disasters.
        Linear equations with miniscule errors intersect erroneously  
   Conjuncting the above 3 premises, we conclude: "Numerical Methods is Hopeless!"
   Not quite!!!        Therefore, Let's begin :)    


Appendix A: Matrix Algebra
A.1 Matrix fundamentals
A.2 Block multiplication
A.3 Eigenvalues and eigenvectors
A.4 Symmetric matrices
A.5 Vector calculus

Appendix B: Introduction to MATLAB   (Hands-on lab session)
B.1 Starting MATLAB
B.2 MATLAB graphics
B.3 Programming in MATLAB
B.4 Flow control
B.5 Functions
B.6 Matrix operations


Chapter 0. Fundamentals
0.1 Evaluating a polynomial
0.2 Binary numbers (Decimal to binary and Binary to decimal)
0.3 Floating point representation of real numbers
   0.3.1 Floating point formats
   0.3.2 Machine representation
   0.3.3 Addition of floating point numbers
0.4 Loss of significance
0.5 Review of calculus


Chapter 1. Solving Equations
1.1 The Bisection Method  (Bracketing a root.  How accurate and how fast?)
1.2 Fixed point iteration (Fixed points of a function, their geometry, convergence, & iteration)
1.3 Limits of accuracy   (Forward & backward error, Wilkinson polynomial, sensitivity, error) 
1.4 Newton’s Method   (Quadratic versus linear convergence of Newton's method)
1.5 Root-finding without derivatives    (Secant method and variants;  Brent's Method)
      REALITY CHECK 1: Kinematics of the Stewart platform
Quiz #1

Chapter 2. Systems of Equations
2.1 Gaussian elimination  (Naive Gaussian elimination, Operation counts)
2.2 The LU factorization  (Backsolving with and Complexity of the LU factorization)
2.3 Sources of error  (Error magnification and condition number, Swamping)
2.4 The PA=LU factorization  (Partial pivoting, Permutation matrices, PA = LU factorization)
      REALITY CHECK 2: The Euler-Bernoulli Beam
2.5 Iterative methods
   2.5.1 Jacobi Method
   2.5.2 Gauss-Seidel Method and SOR
   2.5.3 Convergence of iterative methods
   2.5.4 Sparse matrix computations
2.6 Methods for symmetric positive-definite matrices
   2.6.1 Symmetric positive-definite matrices
   2.6.2 Cholesky factorization
   2.6.3 Conjugate Gradient Method
   2.6.4 Preconditioning
2.7 Nonlinear systems of equations
   2.7.1 Multivariate Newton's method
   2.7.2 Broyden's method
Quiz #2
 
Chapter 3. Interpolation
3.1 Data and interpolating functions
   3.1.1 Lagrange interpolation
   3.1.2 Newton's divided differences
   3.1.3 How many degree d polynomials pass through n points?
   3.1.4 Code for interpolation
   3.1.5 Representing functions by approximating polynomials
3.2 Interpolation error (Interpolation error formula, Newton form, Runge phenomenon)
3.3 Chebyshev interpolation  (Chebyshev's Theorem, Chebyshev polynomials, Interval change)
3.4 Cubic splines   (Properties of splines, Endpoint conditions)
3.5 Bézier curves
      REALITY CHECK 3: Constructing fonts from Bézier splines
Quiz #3
 
Chapter 4. Least Squares
4.1 Least squares and the normal equations   
   4.1.1 Inconsistent systems of equations
   4.1.2 Fitting models to data
   4.1.3 Linear and nonlinear models   (Conditioning of least squares)
4.2 A survey of models   (Periodic data,  Data linearization)  
4.3 QR factorization
   4.3.1 Gram-Schmidt orthogonalization and least squares
   4.3.2 Modified Gram-Schmidt orthogonalization
   4.3.3 Householder reflectors
4.4 Generalized Minimum Residual (GMRES) Method
   4.4.1 Krylov methods
   4.4.2 Preconditioned GMRES
4.5 Nonlinear least squares
   4.5.1 Gauss-Newton method
   4.5.2 Models with nonlinear parameters
   4.5.3 Levenberg-Marquardt method
   REALITY CHECK 4: GPS, conditioning and nonlinear least squares
Quiz # 4

Chapter 5. Numerical Differentiation and Integration
5.1 Numerical differentiation
   5.1.1 Finite difference formulas
   5.1.2 Rounding error
   5.1.3 Extrapolation
   5.1.4 Symbolic differentiation and integration
5.2 Newton-Cotes formulas for numerical integration
   5.2.1 Trapezoid rule
   5.2.2 Simpson's Rule
   5.2.3 Composite Newton-Cotes Formulas
   5.2.4 Open Newton-Cotes methods
5.3 Romberg integration
5.4 Adaptive quadrature
5.5 Gaussian quadrature
   REALITY CHECK 5: Motion control in computer-aided modelling
Quiz #5

Chapter 6. Ordinary Differential Equations
6.1 Initial value problems
   6.1.1 Euler's method    (skim next subchapter)
   6.1.3 First-order linear equations
6.2 Analysis of IVP solvers
   6.2.1 Local and global truncation error
   6.2.2 The explicit trapezoid method
   6.2.3 Taylor methods
6.3 Systems of ordinary differential equations
   6.3.1 Higher order equations
   6.3.2 Computer simulation: The pendulum
   6.3.3 Computer simulation: Orbital mechanics
6.4 Runge-Kutta methods and applications
   6.4.1 The Runge-Kutta family
   6.4.2 Computer simulation: The Hodgkin-Huxley neuron
   6.4.3 Computer simulation: The Lorenz equations
   REALITY CHECK 6: The Tacoma Narrows Bridge
6.5 Variable step-size methods
   6.5.1 Embedded Runge-Kutta pairs
   6.5.2 Order 4/5 methods
6.6 Implicit methods and stiff equations
6.7 Multistep methods
   6.7.1 Generating multistep methods
   6.7.2 Explicit multistep methods
   6.7.3 Implicit multistep methods
Quiz #6

Chapter 7. Boundary Value Problems  (Optional)
7.1 Shooting method
   7.1.1 Solutions of boundary value problems
   7.1.2 Shooting method implementation
   REALITY CHECK 7: Buckling of a circular ring
7.2 Finite difference methods
   7.2.1 Linear boundary value problems
   7.2.2 Nonlinear boundary value problems
7.3 Collocation and the Finite Element Method
   7.3.1 Collocation
   7.3.2 Finite elements and the Galerkin method
 
Chapter 8. Partial Differential Equations  (Optional)
8.1 Parabolic equations (Forward difference, Backward difference, & Crank-Nicolson methods)
8.2 Hyperbolic equations   (The wave equation,  The CFL condition)
8.3 Elliptic equations    ( Finite difference and finite element methods for elliptic equations)
   REALITY CHECK 8: Heat distribution on a cooling fin
8.4 Nonlinear partial differential equations  (Implicit Newton solver, Nonlinearity  in 2D)  
 
Chapter 9. Random Numbers and Applications
9.1 Random numbers  (Pseudo-random numbers, Exponential and normal random numbers)
9.2 Monte-Carlo simulation (Power laws for Monte Carlo estimation, Quasi-random numbers)
9.3 Discrete and continuous Brownian motion  (Random walks, Brownian motion)
9.4 Stochastic differential equations  (Adding noise to diff. eq.,  Numerical methods for SDEs)
   REALITY CHECK 9: The Black-Scholes formula
Quiz #7

Chapter 10. Trigonometric Interpolation and the FFT
10.1 The Fourier Transform   (Complex arithmetic, Discrete Fourier Transform, FFT)
10.2 Trigonometric interpolation  (DFT Interpolation Theorem,  fast trigonometric computation)
10.3 The FFT and signal processing
   10.3.1 Orthogonality and interpolation
   10.3.2 Least squares fitting with trigonometric functions
   10.3.3 Sound, noise, and filtering
   REALITY CHECK 10: The Wiener filter
Quiz #8

Chapter 11. Compression
11.1 The Discrete Cosine Transform
   11.1.1 One-dimensional DCT
   11.1.2 The DCT and least squares approximation
11.2 Two-dimensional DCT and image compression
   11.2.1 Two-dimensional DCT
   11.2.2 Image compression
   11.2.3 Quantization
11.3 Huffman coding
   11.3.1 Information theory and coding
   11.3.2 Huffman coding for the JPEG format
11.4 Modified DCT and audio compression
   11.4.1 Modified Discrete Cosine Transform
   11.4.2 Bit quantization
   REALITY CHECK 11: A simple audio codec using the MDCT
Quiz #9

Chapter 12. Eigenvalues and Singular Values
12.1 Power iteration methods
   12.1.1 Power iteration
   12.1.2 Convergence of power iteration
   12.1.3 Inverse power iteration
   12.1.4 Rayleigh quotient iteration
12.2 QR algorithm
   12.2.1 Simultaneous iteration
   12.2.2 Real Schur form and QR
   12.2.3 Upper Hessenberg form
   REALITY CHECK 12: How search engines (like Google) rate page quality
12.3 Singular value decomposition
   12.3.1 Finding the SVD in general
   12.3.2 Special case: symmetric matrices
12.4 Applications of the SVD
   12.4.1 Properties of the SVD
   12.4.2 Dimension reduction
   12.4.3 Compression
   12.4.4 Calculating the SVD
Quiz #10

Chapter 13. Optimization    (Optional)
13.1 Unconstrained optimization without derivatives
   13.1.1 Golden section search
   13.1.2 Successive parabolic interpolation
   13.1.3 Nelder-Mead search
13.2 Unconstrained optimization with derivatives
   13.2.1 Newton's method
   13.2.2 Steepest descent
   13.2.3 Conjugate gradient search
   13.2.4 Nonlinear least squares
   REALITY CHECK 13: Molecular conformation and numerical optimization

Final Examination
 
9. Teaching Methods (e.g., lecture, discussions, presentations, etc.)

a) Classroom lectures, discussions, and problem solving sessions 
b) Homework reviews 
c) Lab work programming with using compilers, IDE's, & profilers.
10. Course Expectations: 

a. Reading Assignments 
    Item 8 (above) addresses the reading schedule issue. 

b. Tentative timeline for submission of written assignments or other work 
    Projects and class work will be collected as scheduled. 

c. Attendance 
    Attendance will be recorded.  Departmental guidelines require 
            that: 3 absences (2 for night) --->  departmental warning letter 
                   7 absences (4 for night) --->  automatic failure in course 
   Only valid excuses (in writing) allay these consequences. 
   Attendance and success coincide. 

d. Participation in out-of-class activities (e.g. workshops, performances):  Not Applicable
e. Examinations (tentative dates, make-up policy, etc.) 
   All exams will be announced at least one full week in advance. 
   If you are absent on the day an exam is announced, you are  responsible for finding out 
   about it from a fellow student or the professor.  No make-up exams will be given except for 
   extraordinary circumstances. 
   Item 8 (above) addresses the examination schedule issue. 
   Refer to:   http://www.wpunj.edu/registrar/finalexamcalendars/final-exam-spring.dot  
   Final Exam. Period:   Thursday  5/9/2013  at 2:00PM-4:30PM,  Science Hall East 5019 

f. Class participation     
   Bring the specified textbook to each class session. 
   Before lab sessions and lectures, read relevant text to optimize productivity.

11. Grading and other methods for assessing student academic performance
  • Periodic quizzes, the culminating one being a cumulative final examination. 
  • Homework/Programming Assignments 
  • Final Grade  =  (20%) * Assignments  + (60%) * Quizzes  +  (20%) * Final Exam
12. Additional information (Calendar):   

Last day for course withdrawal is  3/5/2013.
Classes will be in session from 1/14/2013 to 5/2/2013, followed by finals week 5/3/13-5/10/13.
    (refer to:  http://www.wpunj.edu/registrar/calendars/spring.dot ).
Holidays:   2/18/13   (Presidents Day)            and     2/21/13 Thursday is a Monday schedule  
                 3/17/13-3/23/13 (Spring Break)   and     3/29/13 (Good Friday).