Program Overview

Course Overview

Course Description

The course Mathematics 1D: Calculus (TMA4401) is a foundation course, level I, that covers various topics in mathematical analysis. The course content includes sequences, completeness property for real numbers, convergence of sequences, continuous functions of one variable, differentiation, integration, Taylor polynomials, and series.

Course Details

• Credits: 7.5
• Level: Foundation courses, level I
• Course Start: Autumn 2025
• Duration: 1 semester
• Language of Instruction: Norwegian
• Location: Trondheim
• Examination Arrangement: School exam

About the Course

Course Content

The course covers the following topics:

• Sequences and completeness property for real numbers
• Convergence of sequences (pointwise and uniform convergence)
• Continuous functions of one variable (continuity, intermediate value theorem, extreme value theorem, and uniform continuity)
• Differentiation of functions of one variable (rules of differentiation, mean value theorem, and optimization of functions)
• Approximation of functions by Taylor polynomials and Taylor's theorem
• Transcendent functions, inverse functions, exponential functions, logarithms, trigonometric functions, and inverse trigonometric functions
• Definite integral of functions of one variable (Riemann sums, fundamental theorem of analysis, and analytical and numerical integration techniques)
• Series (tests for convergence, alternating series, power series, and Taylor series)
• Separable and linear differential equations (existence and uniqueness of solutions, analytical and numerical solution methods, convergence, and error analysis)
• Examples of mathematical modeling and applications in science and technology

Learning Outcome

Upon completing the course, students will be able to:

• Understand and apply basic concepts, results, and methods from one-variable mathematical analysis
• Apply algorithmic thinking to understand and apply basic numerical methods for integration and solving non-linear equations, linear systems of equations, and differential equations
• Analyze numerical methods with regard to applicability and precision
• Use numerical methods in a programming language and understand the possibilities and limitations of various methods
• Formulate, model, and solve simple technological problems relevant to their study program 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 tasks will be assigned during the course.

Evaluation

Examination

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 is recommended.

Course Materials

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

Credit Reductions

The 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.

Subject Areas

• Mathematics
• Technological subjects

Academic Overlap

The course has academic overlap with the following courses:

• SIF5003
• MA1101
• MA1102
• MA6101
• MA6102
• MA0001
• MA0003
• TMA4100
• TMA4101
• TMA4400
• TMA4410
• TMA4411
• TMA4422
• IMAA1002
• IMAG1002
• IMAT1002