Program Overview

Course Overview

The course Mathematics 2B: Linear Algebra, Differential equations, Integral transforms and Series (TMA4411) is a foundation course at level I, worth 7.5 credits. It is scheduled to start in the spring of 2026 and will run for one semester. The language of instruction is Norwegian, and the course will be held in Trondheim.

Course Content

The course builds upon TMA4400 and further develops topics from this course. It covers various forms of infinite series, methods for approximating functions, and integral transforms. Key areas of study include:

• General vector spaces and linear transformations
• Subspaces, linear dependence and independence, and dimensional analysis in R and general vector spaces
• Basis, kernel, and range, rank of matrices, projection, and orthogonalisation
• Orthogonal functions and inner product
• Linear systems of first-order differential equations and numerical methods for ordinary differential equations
• Polar coordinates, functions of several variables, partial derivatives, gradient, directional derivative, maxima, and minima in several variables
• Multiple integrals, coordinate transformations, and the Jacobian determinant
• Examples of mathematical modelling and applications in science and technology

Learning Outcome

Upon completion of the course, students will be able to:

• Understand and apply basic concepts, results, and methods from linear algebra in Euclidean spaces
• Understand and apply basic concepts and methods concerning ordinary differential equations
• Apply knowledge of multivariate mathematical analysis, including optimisation methods and multiple integration, to formulate and solve problems in mathematics and natural science/technology
• Demonstrate algorithmic thinking to understand and apply basic numerical methods for solving ordinary differential equations
• Analyse numerical methods with regard to applicability and precision
• Use numerical methods in a programming language, understanding the possibilities and limitations of the methods
• Formulate, model, and solve simple technological problems relevant to their study programme using analytical and computational methods

Learning Methods and Activities

The course will consist of 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.

Compulsory Assignments

• Compulsory exercises

Evaluation

The grade will be based on a final written exam. In the event of a re-sit exam, the written exam may be changed to an oral exam, which will be held in August.

Recommended Previous Knowledge

TMA4400 - Mathematics 1: Calculus and Linear Algebra, or equivalent.

Course Materials

Course materials will be stated at the start of the semester.

Credit Reductions

This course has academic overlap with several other courses. If a student takes overlapping courses, they will receive a credit reduction in the course where they have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently. A detailed list of overlapping courses and their corresponding credit reductions is available.

Subject Areas

• Mathematics
• Technological subjects

Examination Arrangement

The examination arrangement for this course is a written school exam, with a weighting of 100/100. Examination aids are allowed, as specified by code D. The exam duration is 4 hours, and the exam system used is Inspera Assessment.

Ordinary Examination - Spring 2026

The ordinary examination will take place in the spring of 2026. The exact date, time, and location will be announced, with the location potentially subject to change. Students can find their room location on Studentweb.

Re-sit Examination - Summer 2026

The re-sit examination will be held in the summer of 2026. Details regarding the date, time, and location will be provided closer to the examination period.