Overview
MATH5175 is a special topic in the Applied Mathematics course for honours and postgraduate coursework students. The Topic title for 2026 is Calculus of Variations
Units of credit:Ìý6
Cycle of offering:Â Topics rotate each year
Graduate attributes:Â The course will enhance your research, inquiry and analytical thinking abilities.
More information:Â Â The Course outline will be made available closer to the start of term - please visit this website:Â /course-outlines
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For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.
If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.
The Online Handbook entry contains information about the course.Â
If you are currently enrolled in MATH5175, you can log into  for this course.
Course overview
This course provides a comprehensive introduction to the field of Calculus of Variations, a branch of mathematics that explores the principles governing the optimisation of functionals (function of functions). Calculus of variations is an active area of research with applications in science and technology, e.g. in physics, material science and image processing. Moreover, variational methods play a crucial role in various areas of mathematics such as differential equations, optimisation, geometry and probability theory.
The first part of this course deals with the study of Euler-Lagrange equations, a system of differential equations that arise naturally from variational problems (optimisation of functionals). These equations characterise the solutions to the variational problems. The second part of the this course will use tools from differential equations to characterise properties of the solutions to variational problems. The course will conclude with a study of the ‘direct method’ which discusses the existence of solutions to variational problems.