# Syllabus for Single Variable Calculus

Envariabelanalys

## Syllabus

• 10 credits
• Course code: 1MA013
• Education cycle: First cycle
• Main field(s) of study and in-depth level: Mathematics G1F
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2007-03-19
• Established by:
• Revised: 2018-10-30
• Revised by: The Faculty Board of Science and Technology
• Applies from: week 30, 2019
• Entry requirements: One of the courses Basic Course in Mathematics, Algebra and Vector Geometry or Algebra and Geometry (these courses may be read in parallell with 1MA013).
• Responsible department: Department of Mathematics

## Learning outcomes

In order to pass the course (grade 3) the student should be able to

• give an account of the concepts of limit, continuity, derivative and integral;
• use the differentiation rules and use the derivative in optimisation problems;
• reproduce a number of standard limits and how to use them in computations;
• use different integration techniques;
• use integrals for the computation of areas, volumes and arc lenghts;
• give an account of and use some basic concepts in the theory of infinite series;
• compute Taylor expansions of elementary functions;
• solve linear differential equations with constant coefficients, first order linear differential equations using integrating factors and separable differential equations;
• exemplify and interpret important concepts in specific cases;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• present mathematical arguments to others.

## Content

Functions: monotonicity and inverse. Inverse trigonometric functions. Limits and continuity: notions and rules. The derivative: notions, differentiation rules, the chain rule, the mean value theorem and applications. Extreme value problems. Curve sketching. The integral: definite integral, primitive function, the fundamental theorem of integral calculus. Integration techniques: substitutions, integration by parts, integrals of rational functions. Improper integrals. Applications of integration: area, volume and arc length. Taylor's formula with applications.
Numerical series: convergence, convergence criteria for positive series, absolute convergence.
Convergence criteria for improper integrals. Power series. Ordinary differential equations: existence and uniqueness of solutions. Linear differential equations with constant coefficients. Solvable types of differential equations : separable equations and integrating factors.

## Instruction

Lectures and problem solving sessions. Assignments.

## Assessment

Written examination at the end of the course (8 credits). Written and oral assignments (2 credits).

## Other directives

The course may not be included in the same higher education qualifications as Derivatives and Integrals, Series and Ordinary Differential Equations, and Calculus for Engineers.

## Reading list

Applies from: week 01, 2019

• Adams, Robert A.; Essex, Christopher Calculus : a complete course

9. ed.: Toronto: Pearson Addison Wesley, 2017

Find in the library

Mandatory