Course content

The course is based on TMA4400 and TMA4410 and develops topics from these courses further. New topics are integral transforms and functions of several variables including multiple integrals. The course continues the study of Fourier analysis and of numerical linear algebra.

Integral transforms: Laplace and Fourier transforms.

Functions of several variables: partial derivatives, gradient, directional derivative, vector functions. Extremal value problems in several variables. Lagrange's method of multipliers. Optimisation theory. Newton's method in several variables. Parametrized curves and surfaces. Double and triple integral, line integral, surface integral. Least squares method, rotation matrices, singular value decomposition.

Examples of mathematical modeling and applications within science and technology.

Learning outcome

The student understands and can apply basic notions, results, and methods in the theory of integral transforms, and can use them in different situations.

The student understands and can apply basic notions, results, and methods from multivariable calculus, including optimization methods, multiple integrals, line integrals, and surface integrals. The student can use the least squares method in order to solve overdetermined systems both analytically and numerically. In addition, the student can analyze the different numerical methods in terms of applicability and precision and understands the possibilities and limitations of the methods regarding the different problems they are applied to.

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, TMA4410 - Mathematics 2A, or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions