Course content

The course builds upon TMA4400, TMA4411, and TMA4421, and further develops topics from these courses. It discusses the Laplace transform for the solution of ordinary differential equations, and Fourier analysis as a new method for the representation and approximation of functions. The course provides an introduction to the field of partial differential equations, where it discusses both theory and numerical solution methods. In addition, the course introduces modern methods in machine learning including matrix and tensor factorisation and neural networks.

Laplace transform and solution of ordinary differential equations; Fourier series; Fourier transformation; discrete Fourier transformation; partial differential equations; finite differences for the solution of partial differential equations; matrix and tensor factorisation; neural networks. Introduction to computational tools with examples.

Learning outcome

The student understands basic notions, results, and methods from the theory of integral transforms and can use them in different settings including the solution of ordinary differential equations and approximation of functions.

The student has basic knowledge about the theory of partial differential equations and is familiar with analytic solution methods in simple cases. The student is familiar with the finite difference method for the numerical solution of partial differential equations.

The student is familiar with the underlying principles of modern methods in machine learning and has a basic understanding of the architecture and training of neural networks.

The student can use analytical and computational methods to formulate, model, and solve simple technological problems relevant to their study programme.

The course will primarily contribute to competence area K1, show specialist knowledge and a professionally grounded perspective. It will also contribute to competence area K2, analyzing engineering problems in collaboration with the individual study programmes that the course serves.

Learning methods and activities

Lectures and compulsory exercises. The number of exercises that must be approved will be stated at the start of the semester on the course's website. The course or parts of it may be taught in English.

Compulsory assignments

• Obligatoric exercises

Recommended previous knowledge

TMA4400 - Mathematics 1, TMA4411 - Mathematics 2B, TMA4421 - Mathematics 3B, or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions