course-details-portlet

TMA4400

Mathematics 1: Calculus and Linear Algebra

New from the academic year 2025/2026

Credits 7.5
Level Foundation courses, level I
Course start Autumn 2025
Duration 1 semester
Language of instruction Norwegian
Location Trondheim
Examination arrangement Written school exam

About

About the course

Course content

The course is a deepening and continuation of subject matter on functions and vectors from upper secondary school and it forms the foundation for the other mathematics courses in the Master of Technology study programmes.

Number sets (from natural to complex numbers). The limit concept, convergence of sequences, completeness of the real numbers. Properties and theorems connected to functions of one real variable: Continuity, the Intermediate-Value Theorem, the Mean-Value Theorem. Optimisation of functions (max/min problems). Approximation of functions with Taylor polynomials.

Systems of linear equations. Linear dependence and independence, and dimensional analysis (in R3). Gauss elimination and iterative methods. Matrices and determinants. Eigenvalues and eigenvectors. Banach's fixed-point theorem for matrices. Difference equations.

The derivative of functions of one real variable. Composite functions. Differentiation rules. The definite integral of functions of one real variable. Riemann sums. The Fundamental Theorem of Calculus. Analytical and numerical integration methods

Numerical solution of algebraic equations. Convergence and error analysis.

Separable and linear differential equations. Existence and uniqueness of solutions. Analytical and numerical solution methods. Convergence and error analysis.

Examples of mathematical modelling and applications in science and technology.

Learning outcome

The student understands and can apply basic concepts, results and methods from one-variable mathematical analysis related to limits, continuity, differentiation, integration, convergence of sequences, and Taylor polynomials. The student understands and can apply basic concepts and methods concerning linear systems of equations and matrices. The student has knowledge about algorithmic thinking in order to understand and apply basic numerical methods for integration and for solving non-linear equations, linear systems of equations and differential equations. The student can analyse such methods with regard to applicability and precision.

The student is familiar with the use of numerical methods in a programming language and understands the possibilities and limitations of the various methods in relation to the 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; analysing engineering problems, in collaboration with the various study programmes that the subject 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 will be taught in Norwegian.

Compulsory assignments

  • Compulsory exercises

Further on 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. The re-sit exam will be held in August.

Course materials

Stated at the start of the semester.

Credit reductions

Course code Reduction From
TMA4110 2 sp Autumn 2025
TMA4100 5.5 sp Autumn 2025
TMA4101 7.5 sp Autumn 2025
TMA4115 2 sp Autumn 2025
MA0001 3.7 sp Autumn 2025
MA1101 5 sp Autumn 2025
MA6101 5 sp Autumn 2025
MA1102 2.5 sp Autumn 2025
MA6102 2.5 sp Autumn 2025
MA1201 2.5 sp Autumn 2025
MA6201 2.5 sp Autumn 2025
IMAA1002 4 sp Autumn 2025
IMAG1002 4 sp Autumn 2025
IMAT1002 4 sp Autumn 2025
TMA4401 5 sp Autumn 2025
TMA4413 2.5 sp Autumn 2025
This course has academic overlap with the courses in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics
  • Technological subjects

Examination

Examination

Examination arrangement: Written school exam
Grade: Letter grades

Ordinary examination - Autumn 2025

Written school exam
Weighting 100/100 Examination aids Code D Date 2025-12-01 Time 09:00 Duration 4 hours Exam system Inspera Assessment
Place and room for written school exam

The specified room can be changed and the final location will be ready no later than 3 days before the exam. You can find your room location on Studentweb.

Sluppenvegen 14
Room SL110 lilla sone
64 candidates
Room SL110 turkis sone
73 candidates
Room SL310 turkis sone
19 candidates
Room SL111 brun sone
81 candidates
Room SL410 orange sone
58 candidates
Room SL311 grønn sone
68 candidates
Room SL110 hvit sone
64 candidates
Room SL430
54 candidates
Room SL111 blå sone
36 candidates
Room SL410 blå sone
51 candidates
Room SL111 orange sone
60 candidates
Room SL111 grønn sone
50 candidates
Room SL111 lyseblå sone
72 candidates

Re-sit examination - Summer 2026

Written school exam
Weighting 100/100 Examination aids Code D Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.