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 techniques.
Calculus of Variations (MATH 479)
Programs\Type | Required | Core Elective | Area Elective |
Electronics Engineering | * | ||
Electronics Engineering | * | ||
Industrial Engineering | * | ||
Industrial Engineering (Previous Name: Manufacturing Systems Engineering) | * | ||
Materials Science and Nano Engineering | * | ||
Materials Science and Nano Engineering (Previous Name: Materials Science and Engineering) | * | ||
Mathematics Minor | * | ||
Mechatronics Engineering | * | ||
Mechatronics Engineering | * | ||
Microelectronics | * | ||
Physics Minor | * | ||
Telecommunications | * |
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.
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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. |