Announcements
Please do the COURSE EVALUATIONS.
OH are as normal through Wednesday, 12/10.
HW 7 due date is flexible; term paper due date is not.
There is a ton of helpful material below! The optional HW 8 has been posted.
The final exam will be on Monday, 12/15 from 10:30am-12:30pm in our classroom.
Repository of Old Exam Problems (helpful?)
Syllabus (8/26)
Term Paper (DUE 12/1)
J. Bell’s Course Notes
Desmos Grapher
Week 1 (8/27) - Syllabus and PDE Intro
HW 1 (due 9/3 in class)
Read by 9/1: DuZ: 1.1; Bell 1 and 3
Read by 9/3: DuZ: 1.2-1.4; Bell 2
Read by 9/8: DuZ: 1.5-1.6
HW 1 Solutions
Week 2 (9/1) - Intro. and Classification
Read by 9/8: Bell 4
HW 2 (due: 9/10)
Lecture 1 and 2 slides
Some helpful notes:
Week 3 (9/8) - Brief Classification Examples; Transport and Method of Characteristics
Read by 9/15: DuZ 7.1-7.2
HW 3 (Due: 9/22)
Some helpful notes on characteristics:
Week 4 (9/15) - General First Order, Nonlinearity, Shocks
Read by 9/22: DuZ 7.3
Read by 9/24: Bell 5 and 6
Some helpful content:
HW 3 #6 Solution Movie and Explanation
Some Interesting Notes
Week 5 (9/22) - Begin Wave Equation: Derivation, Operator Factoring; d'Alembert
Read by 10/2: Bell 7
Reference: Strauss: 2.1 and 2.2
HW 4 (Due: ~ 10/3)
Week 6 (9/29) - Interpretation and Qualitative Properties for WEQ
Read by 10/7: Bell 8
Verifying d'Alembert
Examples for the wave equation, and peripheral notes.
HW 4 Help and Optional Videos
Duhamel's principle
Help on VERIFIYING
Dispersion for WEQ and HEQ
Week 7 (10/6) - Finite Energy Wave Uniqueness; Introduce and ``Solve" HEQ
HW 5 (due ~10/17)
Read by 10/13: Bell 9
Reference: Strauss: 3.2, 3.4
Week 8 (10/13) - Solving the HEQ and Basic Properties
Read by 10/23: Bell 10
Reference: Strauss: 2.5, 9.1, 9.2
Gaussians, Convolutions, and HEQ
HW 5 Help: How not to do 5(b)
HW Help Lecture
Duhamel's principle for Heat
Heat Activity I Complete Solutions
Week 9 (10/20) - Finish HEQ Qualitative Properties; Begin Fourier Transform
Read by 10/27: Bell 11
Read by 10/29: DuZ 4.1 - 4.3
Activity for This Week
Heat Activity II Solutions
Comparing Wave and Heat NOTES
Optional COVID-times Video (great for studying; funny): Comparing Heat and Wave Dynamics
Week 10 (10/27) - Integral Transforms; Using Fourier to Solve PDEs
HW 6 (due 11/12)
Read by 11/3: Bell 12 and 13, DuZ 5.2
For Reference: DuZ 5.1, 5.3, and 5.4
Review of the Laplace Transform (optional)
Laplace Transform Table
Week 11 (11/3) - Half-space Problems
Read by 11/10: DuZ 5.2
Read by 11/12: Bell 14 and 15
For Reference: Strauss Ch. 4
Helpful Notes for Half Space Problems
Really Helpful Notes...
Optional Video: Method of Reflection for Heat
Optional Video: Using the Laplace Transform to Solve an IBVP
Week 12 (11/10) - Finish Half-Space Problems; Start Bounded Domains and Separation
HW 7 (due W, 12/3)
Read by 12/1: Bell 16
For Reference: Strauss Ch. 4 and 5
Second Order Methods for Unbounded Domains
Week 13 (11/17) - EVPs and Putting it All Together
Required Videos on Separation and EVPs
Optional Videos Putting It All Together
Week 14 (11/24) - Fourier Theory
Read by 12/3: Bell 17, 18
Lecture Notes for Fourier
Summary Notes and Practice Worksheet for Fourier
Week 15 and 16 (12/2 and 12/9) - Finish Fourier; Qualitative Properties on [0,L]; Higher Dimensions
Read by 12/8: Bell 19, 21
(Optional) HW 8 (due W, 12/12)