Course syllabus

Course MMAT5260
 
Title Calculus of Variations
 
Units 3
 
Lecturer Dr. Liu Chun Lung Kelvin
Office : Rm 202A, LSB
Office number : 3943 7969
Email : clliu@math.cuhk.edu.hk

 
Teaching assistant Fung Tsz Hin Antony
Office : Rm 232, LSB
Office number : 3943 5294
Email : thfung@math.cuhk.edu.hk

 
Prerequisite The prerequisite of this course is calculus and advanced calculus. Specifically, differentiation, Taylor’s expansion, integration, partial differentiation, Lagrange multipliers and some basic techniques of solving ordinary differential equations are required.
 
Course Description In calculus of variations, extremal problems for integral functionals on spaces of functions are studied. Motivated by applications in geometry and physics, this branch of analysis was cultivated by the old masters including Fermat, Newton, Euler and Lagrange and it has been studied intensively ever since. In calculus, differentiation theory is applied to study extremal problems in the Euclidean space which is of finite dimension. In calculus of variations, a parallel study on infinite dimensional space–-the space of functions-–will be carried out.
 
Textbook (Lecture Notes) The Calculus of Variations, by Prof. Kai-Seng Chou, 2014
 
Major Topics
  1. The Euler-Lagrange equation
  2. Generalizations of the Euler-Lagrange equation
  3. Isoperimetric problems
  4. Generalizations of the isoperimetric problems
  5. Variable end-points: general variation formulas
  6. The Legendre condition
Additional Topics If time permits, we will also cover some of the following topics :
  1. Holonomic constraints
  2. Non-holonomic constraints
  3. Jacobi's necessary condition
  4. The Hamiltonian formulation
  5. Noether's Theorem
Reading Reference books are :
 
Assessment
Homeworks 20%
Midterm 30%
Final 50%

 
Homeworks Homeworks will be posted on the course homework page.
 
Examinations There will be one midterm exam and one final exam given during the classes; please see the calendar page for the dates of the exams. No notes (or books) will be allowed during the exams.
 
Honesty in Academic Work The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University.
Although cases of cheating or plagiarism are rare at the University, everyone should make himself/herself familiar with the content of the following website :
http://www.cuhk.edu.hk/policy/academichonesty/
and thereby help avoid any practice that would not be acceptable.