Calculus of Variations
3
In person
MW 10:30-11:50
Wachman Hall 617
Wachman Hall 616
MW 1-2pm
W 3-4pm
Lecture notes and HW assignments will be posted on Canvas
A: 90-100
A-: 85-89
B+: 80-84
B: 70-79
B-: 65-69
C+:60-64
C: 50-59
Undergraduate ODE, Linear Algebra, Calculus sequence, including Advanced Calculus (aka Analysis)
The goal of the course is to introduce students to the fertile ideas of Calculus of Variations and show how they naturally gave rise to many areas of modern mathematics
Variational problems. First variation, Euler-Lagrange
equations. Transversality conditions. Least action principle and
analytical mechanics. Variational symmetries and Noether's
theorem. Conservation of energy, momentum, angular momentum. Weak and
strong local minima. Second variation. Weierstrass needle variation,
and Weierstrass convexity condition. Caratheodory's ``royal
road''. Global Hamiltonians and Hamilton-Jacobi equations. Jacobi
theory of second variation and Weierstrass ``field
theory''. Symplectic structure of Hamilton's equations. Symmetries and
conservation laws in the language of Hamiltonians. Optimal control
problems and Pontryagin's maximum principle. Numerous examples and
applications will be illustrating the above theoretical concepts
throughout the course.
There will be no exams. Your grade will be determined by your HWs
Mandatory
To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.
It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse.
Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.
During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).
The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.
The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).
The following academic support services are available to students (all links open in a new tab/window):
The Math Consulting Center
Student Success Center
University Libraries
Undergraduate Research Support
Career Center
Tuttleman Counseling Services
Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.