The calculus of variations concerns problems in which one wishes to find the minima or extrema of some quantity over a system that has functional degrees of freedom. Many important problems arise in this way across pure and applied mathematics and physics. They range from the problem in geometry of finding the shape of a soap bubble, a surface that minimizes its surface area, to finding the configuration of a piece of elastic that minimises its energy. Perhaps most importantly, the principle of least action is now the standard way to formulate the laws of mechanics and basic physics. In this course it is shown that such variational problems give rise to a system of differential equations, the Euler-Lagrange equations Furthermore, the minimizing principle that underlies these equations leads to direct methods for analysing the solutions to these equations. These methods have far reaching applications and will help develop students’ mathematical technique.
Calculus of Variations (MATH 579)
Programs\Type | Required | Core Elective | Area Elective |
Computer Science and Engineering - With Bachelor's Degree | * | ||
Computer Science and Engineering - With Master's Degree | * | ||
Computer Science and Engineering - With Thesis | * | ||
Cyber Security - With Bachelor's Degree | * | ||
Cyber Security - With Master's Degree | * | ||
Cyber Security - With Thesis | * | ||
Electronics Engineering and Computer Science - With Bachelor's Degree | * | ||
Electronics Engineering and Computer Science - With Master's Degree | * | ||
Electronics Engineering and Computer Science - With Thesis | * | ||
Electronics Engineering - With Bachelor's Degree | * | ||
Electronics Engineering - With Master's Degree | * | ||
Electronics Engineering - With Thesis | * | ||
Energy Technologies and Management-With Thesis | * | ||
Industrial Engineering - With Bachelor's Degree | * | ||
Industrial Engineering - With Master's Degree | * | ||
Industrial Engineering - With Thesis | * | ||
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis | * | ||
Leaders for Industry Computer Science and Engineering - Non Thesis | * | ||
Leaders for Industry Electronics Engineering and Computer Science - Non Thesis | * | ||
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Leaders for Industry Materials Science and Engineering - Non Thesis | * | ||
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Manufacturing Engineering - Non Thesis | * | ||
Manufacturing Engineering - With Bachelor's Degree | * | ||
Manufacturing Engineering - With Master's Degree | * | ||
Manufacturing Engineering - With Thesis | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) | * | ||
Mechatronics Engineering - With Bachelor's Degree | * | ||
Mechatronics Engineering - With Master's Degree | * | ||
Mechatronics Engineering - With Thesis | * | ||
Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) | * | ||
Physics - Non Thesis | * | ||
Physics - With Bachelor's Degree | * | ||
Physics - With Master's Degree | * |
CONTENT
OBJECTIVE
Students will learn rigorous results in the classical and modern one-dimensional calculus of variations and see possible behaviour and application of these results in examples. Also, they will be able to formulate variational problems and analyse them.
LEARNING OUTCOMES
- Learn rigorous results in the classical and modern one-dimensional calculus of variations.
- See possible behaviour and application of these results in examples.
- Formulate variational problems and analyse them.
Update Date:
ASSESSMENT METHODS and CRITERIA
Percentage (%) | |
Midterm | 70 |
Assignment | 30 |
RECOMENDED or REQUIRED READINGS
Readings |
1. U. Brechtken-Manderscheid, Introduction to the Calculus of Variations, Chapman & Hall, 1991. |