ACM 106c

Topics

Finite difference method, finite element method, finite volume method.

Instructor

Lexing Ying
lexing at acm.caltech.edu
305 Firestone
Office hours: Tuesday and Thursday 4-4:30pm

Lectures: Tuesday and Thursday 2:30-4:00pm in 306 Firestone

Teaching Assistants

Peter Stobbe
stobbe at acm.caltech.edu
315 Guggenheim
Office hours: Monday 3-4pm

Recitations: Wednesday noon-1pm

Suggested Texts

Author: Arieh Iserles
Title: A First Course in the Numerical Analysis of Differential Equations
ISBN: 0521556554
Edition: 1
Publisher: Cambridge University Press

Author: John C. Strikwerda
Title: Finite Difference Schemes And Partial Differential Equations
ISBN: 0898715679
Edition: 2
Publisher: Society for Industrial and Applied Mathematics

Author: Dietrich Braess
Title: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics
ISBN: 0521011957
Edition: 2
Publisher: Cambridge University Press

Author: Randall J. LeVeque
Title: Finite Volume Methods for Hyperbolic Problems
ISBN: 0521009243
Edition: 1
Publisher: Cambridge University Press

Author: Alfio Quarteroni and Alberto Valli
Title: Numerical Approximation of Partial Differential Equations
ISBN: 3540571116
Edition: 1
Publisher: Springer

Author: Alexandre Ern and Jean-Luc Guermond
Title: Theory and Practice of Finite Elements
ISBN: 0387205748
Edition: 1
Publisher: Springer

Author: Lawrence C. Evans
Title: Partial Differential Equations
ISBN: 0821807722
Edition: 1
Publisher: American Mathematical Society

Exams, Homework and Grades

Homework will include theoretical assignments, as well as computational assignments which should be implemented either in Matlab or in a programming language such as Fortran, C or C++. Questions relating to homework sets or any other issues arising in the class should be directed to either the TA or the instructor. Collaboration concerning the homework problems is permitted, but each solution set should be primarily the result of the individual work of each student.

There will be two take-home exams, in which collaboration will not be permitted. Both the midterm and final exams will feature problems of a level of difficulty similar to that of those assigned as homework. The programming assigments in the exams will be of a level of difficulty higher than those in the weekly homework sets.

Midterm Exam: the grade in the midterm exam will make up 30% of the final course grade. The midterm exam will contain a combination of theoretical and computational problems.

Final Exam: the grade in the final exam will make up 30% of the final course grade. The final exam will be comprehensive: it will contain a selection of problems on topics covered throughout the course. Like the midterm, the final exam will contain a combination of theoretical and computational problems.

Problem Set & Exam Schedule

Notes

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