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Theory of Partial Differential Equations: Fall 2016

Math 412

Classes TR 9:35 - 10:50 am in Bloc 160
Office Hours M-Tu 1:30 - 2:30pm.
Textbook Richard Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, (5th edition)
Additional info Syllabus, Syllabus Addendum.

Important Notifications

  • There will be no class on Nov 8. The homework are due Nov 10. They might take more time than usual.
  • The midterm exam is on October 18. The topics covered are those from Week 1 - 6 (i.e. homeworks 1-6).
  • The exam 2 is on December 1. The topics covered are those from Week 7 - 11 (i.e. homeworks 7-12).

Important Dates

  • Midterm Exam : October 18
  • Exam 2 : December 1
  • Final: December 9, 12:30 - 2:30 pm.

Extra material

The second exam together with the solutions can be downloaded here.

Here are the snapshots of the fourier series I discussed in class:

Homeworks (Due September 6)

Chapter 1.3 1, 3
Chapter 1.4 1(b and g), 3,10
Chapter 1.5 5,8,11,14 + Read appendix if needed
Return only (excuse my french) 1.4.3 and 1.4.10
Honors + 1.5.8 and 1.5.14

Homeworks II (Due September 13)

Chapter 2 2.2, 3.2(a and c), 3.3 (a,b and d), 3.5, 4.3, 4.4
turn in 2.3.3 (b), 2.4.3
Honors + 2.4.6 and 2.3.3 (d)

Homeworks III (Due September 20)

Chapter 2 4.4 (again), 4.6, 4.7(b), 5.3(a)
turn in 2.4.7(b)
Honors + 2.5.3(a)

Homeworks IV (Due September 27)

Chapter 3 2.1 (a,c,e), 2.4, 3.4,3.9, 3.18, 4.6,4.7
turn in 2.1(e) and compute the fourier serie for the function in 2.1(c)
Honors + 3.4.7

Homeworks V (Due October 4)

Chapter 3 4.8 and 4.12 Hint: in both exercises do not look for a cosine series but use the appropriate extension (which leads to the cosine series), 4.9, 6.1
turn in 4.12 but do not look directly for a cosine series, instead find the apropriate extension.
Honors + Read Section 3.5 and exercise 3.5.1

Homeworks VI (Due October 11)

Chapter 4 4.3 but use the technique discussed in class (extension...), 4.7, 4.8, 4.9, 4.12
Chapter 8 5.3, 5.4, 5.5(b)
turn in 4.4.3
Honors + 8.5.3

Homeworks VII (Not collected)

Chapter 10 2.1, 2.2, 3.1(a), 3.2(a), 3.8, 4.3(a)

Homeworks VIII (due Nov 1)

Chapter 10 6.1(a), 6.10.
turn in all
Honors + none

Homeworks IX (due Nov 10)

Chapter 10 5.1, 5.2, 5.12, 5.17
Chapter 12 2.2, 2.5(a)
turn in 5.12, 12.2.2, 12.2.5(a)
Honors + 5.6, 5.17

Homeworks X (due Nov 17)

Chapter 12 2.3, 2.5(b), 2.7, 3.1, 3.4,
turn in 2.5(b)
Honors + 2.7

Homeworks XI (no need to return)

Chapter 12 4.2, 4.3, 6.1(all), 6.4
turn in none
Honors + none

Homeworks XII (Due November 29 - optional but would replace one of your bad hw)

Chapter 12 6.7(a,c,d), 6.9(a), 6.16, 6.18
turn in 6.18 (a,b)
Honors + none

Material Covered week after week

Week 1 Syllabus, Sections 1.1, 1.2, 1.3, 1.4, 1.5
Week 2 Sections 2.1, 2.3.1, 2.3.2, 2.3.3, 2.3.4, 2.2, 2.3.5
Week 3 Sections 2.4, 2.5.1 and 2.5.2
Week 4 Sections 3.1,3.2,3.3,3.4
Week 5 Sections 3.4, 3.6 + own notes about using the fourier series to solve the 1D heat equation.
Week 6 Sections 4.1, 4.2, 4.3, 4.4, 8.5
Week 7 Sections 10.1, 10.2, 10.3
Week 8 Midterm + Sections 10.3, 10.4
Week 9 Midterm solutions + Sections 10.6.1 + 10.5.2
Week 10 10.5.3, 10.5.4, 10.5.5, 10.6.3, 12.1, 12.2.2, 12.3.1, 12.3.2
Week 11 12.3.3, 12.4, 12.5, 12.6.1, 12.6.2, 12.6.3, 12.6.4
Week 12 6.1, 6.2, 6.3.1, 6.3.2, 6.3.3 + Exam 2