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 L^2 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 R^n
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