# TMA4100 - Calculus 1

### Examination arrangement

Examination arrangement: Portfolio assessment

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 80/100 4 hours C
Work 20/100

### 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, compulsory exercises. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination (80%) and exercises (20%). The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. The exercises only count if they have a positive effect on the final grade.
Retake of examination may be given as an oral examination.

• Exercises

### Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

### Course materials

Will be announced at the start of the course.

### Credit reductions

Course code Reduction From To
MA0001 6.0 2009-01-01
MA0003 6.0 2009-01-01
MA1101 3.7
MA1102 3.7
MA6101 3.7 2009-09-01
MA6102 3.7
SIF5003 7.5

# Examination

Examination arrangement: Portfolio assessment

Term Evaluation form Weighting Examination aids Date Time Room *
Autumn Work 20/100
Autumn Written examination 80/100 C 2016-12-20 09:00 Møterom 8 , R D1-185 Datasal , Møterom 1B , R73 , R41 , Møterom 1C , Møterom 1A , K4 , A , D2 , D1 , C , E6 , E5 , E4 , E3 , E2 , E1 , K3
Summer Work 20/100
Summer Written examination 80/100 C H3 Datalab 524 (Fraggle)
* 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.