Course - Mathematics 1: Calculus and Linear Algebra - TMA4400
Mathematics 1: Calculus and Linear Algebra
New from the academic year 2025/2026
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.
Recommended previous knowledge
Mathematics R2 from upper secondary school, or equivalent knowledge.
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 |
Subject areas
- Mathematics
- Technological subjects
Contact information
Course coordinator
Lecturers
- André Jürgen Massing
- Eduardo Ortega Esparza
- Emilie Lyse Olsen
- Frode Rønning
- Morten Andreas Nome
- Sigrid Grepstad
Department with academic responsibility
Examination
Examination
Ordinary examination - Autumn 2025
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.