Course syllabus for Calculus, part A

Course syllabus adopted 2024-02-06 by Head of Programme (or corresponding).

Observe
Note – can not be included in a Chalmers' degree

Overview

  • Swedish nameMatematik, del A
  • CodeMVE725
  • Credits7.5 Pre-education credits
  • OwnerZBASS
  • Education cyclePre-university
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 95118
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0124 Examination 7.5 fup
Grading: TH		7.5 fup

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level studies

Specific entry requirements

Mathematics 2a or 2b or 2c or equivalent and English 6

Course specific prerequisites

Examination certificate from upper secondary school including or complemented by the courses 2a or 2b or 2c in mathematics.

Aim

The aim of the course is to give basic knowledge in mathematical analysis. The course will also supply a good base for further studies.

Learning outcomes (after completion of the course the student should be able to)

  • understand the structure and formal language of mathematics.
  • be familiar with and use the rules for real numbers and fractions.
  • be familiar with and use the rules for exponents and roots.
  • be familiar with and use the square and conjugate rules, and their generalization to higher powers.
  • be able to solve second degree equations and use the method of completing the square.
  • handle polynomials and divide polynomials.
  • be familiar with the factor theorem and use it to simplify algebraic expressions.
  • solve algebraic equations.
  • handle and describe lines in the plane.
  • solve systems of linear equations.
  • be familiar with fundamental facts about analytic geometry in the plane and in space.
  • define the trigonometric functions and be familiar with some elementary trigonometric identities.
  • solve simpler trigonometric equations.
  • be familiar and handle the concepts of similarity and scales.
  • handle and solve inequalities.
  • define and use absolute value.

Content

  • Foundation of mathematics with axioms, definitions, statements, logic and theorems.
  • Laws for real numbers and fractions.
  • Laws for exponents and roots.
  • Polynomials and rational expressions.
  • Roots to first- and second order equations.
  • Completing the square.
  • Factoring and division of polynomials.
  • Algebraic equations.
  • Lines in the plane.
  • Systems of linear equations and the method of elimination.
  • Some fundamental geometry in the plane and space.
  • Proportionality, scale and uniformity.
  • Inequalities.
  • Absolute value.

Organisation

Teaching takes place through lectures and exercises.

Literature

Håkan Blomqvist: Matematik för tekniskt basår, del 1-3, Matematiklitteratur.

Examination including compulsory elements

The course is graded through written exam with grading scale TH.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.