TMA4100 - Calculus 1


Examination arrangement

Examination arrangement: Portfolio assessment
Grade: Letters

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

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.

Compulsory assignments

  • Exercises

Further on evaluation

In the case that the student receives an F/Fail as a final grade after both ordinary and re-sit exam, then the student must retake the course in its entirety. Submitted work that counts towards the final grade will also have to be retaken. For more information about grading and evaluation. see «Teaching methods and activities».

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 arrangement: Portfolio assessment

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Autumn ORD Work 20/100
Autumn ORD Written examination 80/100 C
  • * 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.