 Role
 Scientific Computing (MWF 8:309:20, Lowe 216)
 Lectures and Homework
 Video Lectures: Online
 Course Notes: amath581 (Book is optional AMAZON)
 Discussion Board: Catalyst
 Homework: Practice 1 (Due midnight 10/6), HW 1 (Due 10/14), HW 2 (Due 10/28), HW 3 (Due 11/4), HW 4 (Due 11/11), HW 5 (Due 11/22), HW 6 (Due 12/7)
 MATLAB: Student Edition (recommended if you do not have access)
 SCORELATOR: scorelator
 Background resources: Beginning Scientific Computing

 Instruction
 Professor J. Nathan Kutz
 Lewis 118
 Office Hours: TBA
 
 Teaching Assistant: Meghana Velagar
 Office Hours: TBA
 EDGE: TBA skype name "theamath581ta"
 MATLAB on campus
 There is MATLAB access at the ICL lab on campus. You can access this also remotely by following the links to "terminal server".
 Agenda for Lectures and Notes
 9/28 Lecture 1: Notes 1.1, Book 7.1
 9/28 Lecture 2: Notes 1.2, Book 7.2
 9/28 Lecture 3: Notes 1.3, Book 7.4
 9/28 Lecture 4: Notes 1.4, Book 7.5
 9/28 Lecture 5: Notes 1.5, Book 7.6
 9/28 Lecture 6: Notes 2.1, Book 8.1
 9/28 Lecture 7: Notes 2.2, Book 8.2
 9/28 Lecture 8: Notes 2.3, Book 8.3
 9/28 Lecture 9: Notes 2.4, Book 8.4
 9/28 Lecture 10: Notes 2.5, Book 8.5
 9/28 Lecture 11: Notes bvp4c (notes), Book 7.7
 9/28 Lecture 12: Notes A.1, Book 25.4
 9/28 Lecture 13: Notes 3.1, Book 9.1
 9/28 Lecture 14: Notes 3.2, Book 9.2
 9/28 Lecture 15: Notes 3.3, Book 9.3
 9/28 Lecture 16: Notes 3.4, Book 9.4
 9/28 Lecture 17: Notes 3.5, Book 9.5
 9/28 Lecture 18: Notes 3.6, Book 9.6
 9/28 Lecture 19: Notes 4.1, Book 10.1
 9/28 Lecture 20: Notes 4.2, Book 10.2
 9/28 Lecture 21: Notes 4.3, Book 10.3
 9/28 Lecture 22: Notes A.2, Book 25.5
 9/28 Lecture 23: Notes 4.4, Book 10.4
 9/28 Lecture 24: Notes 4.5, Book 10.5
 9/28 Lecture 25: Notes 4.6, Book 10.6
 9/28 Lecture 26: Notes 4.7, Book 10.7
 9/28 Lecture 27: Notes A.3, Book 25.6
 9/28 Lecture 28: Notes 5.1, Book 11.1
 9/28 Lecture 29: Notes 5.2, Book 11.2
 9/28 Lecture 30: Notes PDEtool (notes), Book 11.3
 Prerequisites
 Solid background in ODEs and familiarity with PDEs and MATLAB, or permission.
 Course Description
 Survey of practical numerical solution techniques for ordinary and partial differential equations. Emphasis will be on the implementation of numerical schemes to practical problems of the engineering and physical sciences. Methods for partial differential equations will include finite difference, finite element and spectral techniques. Full use will be made of MATLAB and its built in programming and solving functionality.
 Objectives

How to recognize and solve numerically practical problems which may arise in your research. We will solve some serious problems using the full power of MATLAB's built in functions and routines. This class is geared for those who need to get the basics in scientific computing. All major types of PDEs (parabolic, elliptic, and hyperbolic) will be considered in 1D, 2D and 3D in problems ranging from quantum mechanics to fluid flows.
NOTE: This course is a survey of computational methods. The focus is on the implemention of numerical schemes with significant aid from builtin MATLAB functionality such as FFTs, fast matrix solvers, etc. It is not a course in numerical analysis since our coverage of many technical issues is only cursory. A much more comprehensive and detailed treatment of some of the methods covered here is given in AMATH 584, 585, 586.
 Lecture Notes:
.pdf
 Reference Texts on
Reserve:
 1. R. L. Burden and J. D. Faires, Numerical Analysis (Sixth Edition). Brooks/Cole, 1997.
 2. L. N. Trefethen, Finite Difference and Spectral Methods. (freely available).
 3. L. N. Trefethen, Spectral Methods in MATLAB. SIAM.
 4. L. N. Trefethen and D. Bau, Numerical Linear Algebra. SIAM.
 5. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations. CRC Press.
 6.
D. R. Durran,
Numerical Methods for Wave Equations in
Geophysical
Fluid Dynamics. Springer.
 (1) Solution
Methods for Differential Equations: (2 weeks)
We will begin with ODE solvers applied to both initial and boundary value problems. Our application will be to finding the eigenstates of a quantum mechanical problem or of an optical waveguide.
 (a) Initial value problems
 (b) Euler method, 2nd and 4thorder RungeKutta, AdamsBashford
 (c) Stability and time stepping issues
 (d)
Boundary values problems: shooting/collocation/relaxation
 (2)
Finite Difference Schemes for Partial Differential Equations: (3
weeks)
We will introduce the idea of finitedifferencing of differential operators. Our application will be to two problems: vibrating modes of a drum and the evolution of potential vorticity in an advectiondiffusion problem of fluid mechanics.
 (a) Collocation
 (b) Stability and CFL conditions
 (c) Time and space stepping routines
 (d) Tridiagonal matrix
operations
 (3) Spectral Methods for Partial Differential
Equations: (3 weeks)
Transform methods for PDEs will be introduced with special emphasis given to the FastFourier Transform. We will revisit the potential vorticity in an advectiondiffusion problem of fluid mechanics by using these spectral techniques.
 (a) The FastFourier transform (FFT)
 (b) Chebychev transforms
 (c) Time and space stepping routines
 (d) Numerical
filtering algorithms
 (4) Finite Element Schemes for Partial
Differential Equations: (2 weeks)
For complicated computational domains, the use of a finite element scheme is compulsory. The steadystate flow of a fluid over various airfoils will be considered.
 (a) Mesh generation
 (b) Advanced matrix operations

(c) Boundary conditions
Figure
Dynamics of a repulsive BoseEinstein condensate trapped in a 3D lattice potential. The equation was solved using a filtered spectral method in space and 4thorder RungeKutta in time. By the end of this course, you should be able to perform this numerical simulation.Textbook & Notes
There will be no text for this course. I will provide my notes online for you to download. I have several texts which will be on reserve at the library to look through the different sections.
Syllabus
Grading
Your course grade will be determined entirely from your homework. There will be no exams.On or before the due date of each homework, the final homework must be uploaded to SCORELATOR for grading. SCORELATOR will give you up to five chances to get the results correct. The grade for that homework will be based upon the percentage you have exactly right (compared to my master key). The correctness of your codes will determine 100% of your grade.