Are you a current or former mathematics A-Level student looking for a challenge? This course introduces variational calculus: the field that allows you to design mathematical functions to optimise certain conditions.
Ordinary calculus allows you to find extrema (minima and maxima) of functions. Variational calculus allows you to determine what function will extremise a certain quantity, whether it’s something simple like finding the shortest distance between two points, working out how to arrange a fence to maximise an area or determining the shape taken by a suspended wire. The following examples are explored and solved in this fascinating course that has applications in many fields of applied mathematics and physics, such as classical dynamics, wave theory, fluid dynamics and even general relativity.
Course Content
10 LESSONS
10 HOURS Total Length
Lesson 1
Recap on Standard Calculus
60 minutes
Lesson 2
Multivariate Calculus
60 minutes
Lesson 3
Constrained Optimisation and Lagrange Multipliers, Functionals
60 minutes
Lesson 4
Euler-Lagrange Equation
60 minutes
Lesson 5
Euler-Lagrange Equations for Multiple Functions
60 minutes
Lesson 6
First Integrals
60 minutes
Lesson 7
Physical Applications
60 minutes
Lesson 8
Constrained Variation of Functionals
60 minutes
Lesson 9
Variation with Constrained Functions
60 minutes
Lesson 10
Hamilton’s Principle
60 minutes
Key Skills
Algebra
Functions
Educator
John S
Mathematics Whizz
With an undergraduate and postgraduate degree in mathematics, John now teaches mathematics full time. His passion is to help students further their knowledge and understanding within this subject.
