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

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