Course - Mathematics 1 - Single variable calculus - TMA4100
Mathematics 1 - Single variable calculus
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About the course
Course content
Limits, continuity, differentiation, and integration of functions of one variable. The intermediate value theorem, the mean-value theorem, extreme values, transcendental functions, implicit differentiation, related rates, indeterminate forms, Newton's method. Techniques of integration and numerical integration. Riemann sums, the definite integral, and the fundamental theorem of calculus. Area, volume, arclength, area of surfaces of revolution. Sequences, series, and power series. Taylor series, Taylor's formula. First order separable and linear differential equations. Euler's method. Examples of mathematical modelling and from applications to science, technology, and economy.
Learning outcome
- Knowledge. The student understands and is able to recognize and apply concepts, results, and methods from single-variable analysis which deals with limits, continuity, differentiation, integration, convergence of sequences and series, Taylor polynomials, and Taylor series. The student understands and is able to apply basic numerical methods for solution of nonlinear equations, differential equations, and integration, and is aware of the possibilities and limitations that lie in the use of mathematical software.
- Skills. The student is able to apply his or her knowledge of single-variable mathematical analysis to formulate and solve simple problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.
Learning methods and activities
Lectures and compulsory exercises. Information regarding the number of compulsory exercises that must be approved will be listed on the course website at the start of the course. The lectures may be given in English.
Compulsory assignments
- Exercises
Further on evaluation
Grade based on written final written examination. Retake of examination may be given as an oral examination. The retake exam is in August.
Recommended previous knowledge
Mathematics R2 or 3 MX from upper secondary school.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From |
|---|---|---|
| SIF5003 | 7.5 sp | |
| MA1101 | 3.7 sp | |
| MA1102 | 3.7 sp | |
| MA6102 | 3.7 sp | |
| MA0001 | 6 sp | Spring 2009 |
| MA0003 | 6 sp | Spring 2009 |
| MA6101 | 3.7 sp | Autumn 2009 |
| TMA4101 | 3.7 sp | Autumn 2020 |
Subject areas
- Technological subjects
Contact information
Course coordinator
Lecturers
- Denis Zelent
- Erling Arnold Tønseth Svela
- Frode Rønning
- Gereon Quick
- Jon Wallem Anundsen
- Marius Thaule
- Robin Østern Lien