Syllabus for Math 46

This syllabus is tentative and will be updated irregularly. The list of textbook sections and topics on this web page is overly optimistic. Some of the listed topics will certainly be skipped. The homework page will be updated on the regular basis and it will include the list of sections we actually do cover in class.

Lectures

Sections in Text

Brief Description

Day 1, Monday March 29

Section 1.1

Dimensional analysis

Day 2, Wednesday March 31

Section 1.2

Scaling

Day 3, Thursday April 1

x-hour instead of the lecture on

Friday April 16

Review of linear algebra and ODE

Section 1.3

Review of linear algebra and ODE

Day 4, Friday April 2

Section 4.1

Orthogonal expansions

Day 5, Monday April 5

Section 4.1

Uniform versus L2 convergence

Day 6, Wednesday April 7

Section 4.2

Sturm-Liouville problems

Day 7, Thursday April 8

x-hour

Section 4.2

More facts about Sturm-Liouville

Day 8, Friday April 9

End of the second week of schedule adjustment

Section 4.3.2

Integral equations, Volterra Equations

Day 9, Monday April 12

Final day for electing use of the Non-Recording option

Section 4.3.3 and 4.3.4

Fredholm equations, symmetric kernels

Day 10, Wednesday April 14

Section 4.4.1

Green’s functions, Inverses of differential operators

Friday April 16,

No class, instead we had an x-hour on April 1

 

 

Day 11, Monday April 19

Section 4.4.2-4.4.3

Physical interpretations, Greens Function via Eigen functions

Day 12, Wednesday April 21

Section 4.5.1 and 4.5.2

Distributions and test functions

Thursday April 22

First Midterm Exam

6-8 PM in Carpenter 013

 

 

Day 13, Friday April 23

Section 4.5.3

Distribution solutions to the differential equations

Day 14, Monday April 26

Section 6.1

General discussion of the partial differential equations

Day 15, Wednesday April 28

Section 6.2.1 and Section 6.2.2

Conservation laws, Green’s identities, heat equation in Rn

Day 16, Thursday April 29

x-hour

Section 6.2.3-5

Boundary conditions etc

Day 16, Friday April 30

Section 6.3

Equilibrium equations

Day 17, Monday May 3

Section 6.5.1

Laplace Transform

Day 18, Wednesday May 5

Section 6.5.2

Fourier Transform

Day 19, Friday May 7

Final day for dropping a fourth course without a grade notation of "W" 

Sections 6.5.1 and 6.5.2

Using tables 6.1 and 6.2 in reverse direction

Day 20, Monday May 10

More about transforms if necessary

More about transforms if necessary

Day 21, Wednesday May 12

We start Chapter 3 Calculus of Variations, but it may happen that we decide to look at Chapter 2 Perturbation Methods instead

Sections 3.1.1 and 3.1.2

Functionals and Examples

Thursday May 13

Second Midterm Exam

6-8 PM in Carpenter 013

 

 

Day 22, Friday May 14

Section 3.2.1

Normed Linear Spaces, weak and strong norm

Day 23, Monday May 17

Note that Tuesday May 18 is the final day to withdraw from a course

Sections 3.2.2 and 3.2.3

First variation, Gateaux derivative, necessary conditions for the critical point

Day 24, Wednesday May 19

Section 3.3.1 and 3.3.2

The Euler equation, some examples

Day 25, Friday May 21

Section 3.3.3

First integrals and more examples

Day 26, Monday May 24

Sections 3.4.1 and 3.4.2

Higher derivatives, several functions

Day 27, Wednesday May 26

Section 3.4.2

Natural boundary conditions

Day 28, Friday May 28

Section 3.5.1 and if time permits

Section 3.5.2

Hamilton’s principle and Hamilton’s equations if we have time.

Monday May 31

Memorial Day, No Class

 

 

Day 29, Wednesday June 2

Last day of classes

General Wrap up

General Wrap up

Friday June 4

Final Exam

3-6 PM in Kemeny 105