Course syllabus for Calculus

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematisk analys
  • CodeMVE525
  • Credits7.5 Credits
  • OwnerTIKEL
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 64130
  • Maximum participants50
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0117 Examination 6 c
Grading: TH		 6 c
  • 13 Jan 2024 am J
  • 03 Apr 2024 pm J
  • 23 Aug 2024 pm J
0217 Laboratory 1.5 c
Grading: UG		 1.5 c

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Knowledge corresponding to MVE530 Introductory course in mathematics.

Aim

The course should in a logically coherent manner provide the basic knowledge of calculus necessary for further studies. The course will also create conditions for mathematical treatment of technical problems in the profession.

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

  • construct function graphs and determine a function's maximum and minimum value
  • define the concept of inverse function, determine inverse functions and compute their derivatives
  • define the concepts of antiderivative, definite integral and generalized integral and calculate integrals with the basic rules
  • use the most common methods for solving differential equations
  • interpret integrals geometrically
  • apply their knowledge of derivatives and integrals to simple problems related to their engineering topic
  • use Matlab to assist in the solution of problems related to the content of the course

Content

Local maxima and minima. Maximum and minimum value. Mean value theorem. Extreme Value Problems. Asymptotics. Curve construction. Inverse function. Elementary functions: rational functions, trigonometric functions, inverse trigonometric functions, exponential funtions, logarithmic functions. The order of the exponential, polynomial and logarithmic functions. Integration: antiderivative, the connection between area and antiderivative, area calculation, integral notation, definite integral, partial integration, integration by substitution, integration of rational functions, generalized integrals. Separable differential equations. Linear differential equations of the first order. Examples of problems solved with differential equations. Operators, linear differential equations of higher order with constant coefficients. Basics of Matlab, including basic programming.

Organisation

The teaching consists of lectures, exercises and computer exercises.

Literature

Communicated before the course starts.

Examination including compulsory elements

All but the last two learning outcomes are examined by a written exam. The last two learning outcomes are examined by mandatory exercises in Matlab that have the grade of pass or fail. Optional quizzes that can give bonus points for the exam may occur. The final grade is based on the results of the exam.

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.

The course syllabus contains changes

  • Changes to course rounds:
    • 2023-10-26: Examinator Examinator changed from Joakim Becker (becker) to Thomas Wernstål (twernst) by Viceprefekt
      [Course round 1]
Calculus | Chalmers