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Partial Differential Equations (PDEs) are important in many fields including in mathematics, statistics, natural sciences, engineering and finance. This class will discuss both mathematical foundations and practical solution methods for PDEs. Examples also will be discussed from related applications areas.
Please be sure to read the prerequisites and grading policies for the class. Also see the syllabus for more details.
Prerequisites:
A knowledge of real/complex analysis and linear algebra.
Grading:
The grade for the class will be based on the homework assignments (see policy below), midterm exam, and final exam as follows:
Homework Assignments 30%
Midterm Exam 30%
Final Exam 40%
Homework Policy:
Assignments will be announced in lecture and posted on the class website. Prompt submission of the homework assignments is required. While no late homework submissions will be accepted, one missed assignment will be allowed without penalty. While it is permissible and you are encouraged to discuss materials with classmates, the submitted homework must be your own work. These will be graded by the TA Nico Gonzalez.
| TA | Information | ||
|---|---|---|---|
| Name: | Nico Gonzalez | ||
| Email: | nicogonzalez-at-math.ucsb.edu (replace -at- with @) | ||
| MathLab Hours: | Mondays 5pm - 7pm, South Hall 1607. | ||
| Office Hours: | Fridays 5pm - 7pm, South Hall 6431S. |
Exams:
The midterm exam will be given Tuesday, February 13th.
Supplemental Class Materials:
| Additional Notes: | |||
| (please submit any typos here) | |||
| - Method of Characteristics, Solving First-Order PDEs | [PDF] | ||
| - Classifying Second-Order PDEs and Canonical Forms | [PDF] | ||
| - Wave Equation and Solution Techniques | [PDF] | ||
| - Diffusion Equation and Solution Techniques | [PDF] | ||
| - Separation of Variables | [PDF] | ||
| Codes: Numerical Examples | |||
| - Wave Equation | [jupyter notebook] [PDF] | ||
| - Diffusion Equation | [jupyter notebook] [PDF] | ||
| Other: | |||
| - LaTeX typesetting | [tutorial] [documentation] [summary sheet] | ||
| - Jupyter Notebooks | [python interface] | ||
| - Python | [documentation python 3.11] [general tutorial] [Codecademy] | ||
| Careers: Profiles of people and jobs I | [PDF] | ||
| Careers: Profiles of people and jobs II | [PDF] | ||
| Preparation Materials: | |||
| - Midterm Exam Outline | [PDF] | ||
| - Midterm Exam Practice Problems | [PDF] | ||
| - Midterm Solutions | [PDF] | ||
| - Final Exam Outline | [PDF] | ||
| - Final Practice Problems | [PDF] | ||
Homework Assignments:
Please be sure to turn in all homeworks by 11pm PST on the due date following the instructions on the Canvas/Gradescope page.
HW1: (Due Tuesday, January 16) 1.1: 2ace, 3bdh, 4, 5abde, 6, 7, 9, 11, 12; 1.2: 1, 3, 4, 5, 7, 11, 13.
HW2: (Due Tuesday, January 23) 1.3: 2, 3, 6, 7, 9; 1.4: 2, 4; 1.5: 1, 3, 4, 5.
HW3: (Due Tuesday, January 30) 1.6: 1, 2, 4; 2.1: 2, 3, 7, 8, 11; 2.2: 1, 2, 5.
HW4: (Due Tuesday, February 6) 2.3: 1, 3, 6, 8; 2.4: 1, 4, 6, 15.
HW5: (Due Thursday, February 15) 2.4: 9, 11, 16; 2.5: 1, 2, 3, 4;
HW6: (Due Thursday, February 22) 3.1: 1, 4, 5; 3.2: 1, 2, 3;
HW7: (Due Wednesday, March 6) 3.3: 1, 3; 3.4: 2, 4, 13;
HW8: (Due Thursday, March 14) 4.1: 1, 2, 4; 4.2: 1, 4;