# TMA4100 - Mathematics 1 - Single variable calculus

### Examination arrangement

Examination arrangement: School exam

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours D

### 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

1. 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.
2. 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.

• 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.

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
SIF5003 7.5
MA1101 3.7
MA1102 3.7
MA6102 3.7
MA0001 6.0 SPRING 2009
MA0003 6.0 SPRING 2009
MA6101 3.7 AUTUMN 2009
TMA4101 3.7 AUTUMN 2020
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2024

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
• Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD School exam 100/100
Summer UTS School exam 100/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

More on examinations at NTNU