Course syllabus for Introductory course in calculus

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

Overview

  • Swedish nameInledande matematisk analys
  • CodeMVE595
  • Credits6 Credits
  • OwnerTKSAM
  • 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 58117
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0119 Examination 4.5 c
Grading: TH		4.5 c
  • 26 Okt 2023 pm J
  • 05 Jan 2024 am J
  • 30 Aug 2024 am J
0219 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

Aim

The aim of the course is to give, together with other mathematics courses, a general mathematical education which is as useful as possible for further studies and technical professional work. The course shall, in a logical and holistic manner, provide knowledge of elementary calculus which is necessary for further studies in Civil and Environmental Engineering.

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

After completion of this course, the student should be able to
  •  define and apply the concept of a function and related concepts.
  •  define and identify properties connected to functions, such as increasing, decreasing, one-to-one, maximum, minimum (global and local).
  •  define invertibility and inverse function, and calculate an inverse function.
  •  handle the basic elementary functions and be familiar with their properties and the corresponding algebraic rules.
  •  understand and apply the concept of a limit of a function as the independent variable tends to a finite number or to plus/minus infinity, as well as the corresponding task for improper limits.
  •  derive the most important "standard limits" and use the limit laws and "standard limits" to calculate new limits.
  •  define the concept of continuity, and use the intermediate value theorem and the max-min-theorem for functions continuous on bounded and closed intervals.
  •  define the concepts of a differentiable function and its derivative and give interpretations of the meaning of the derivative, e.g. to express rates of change.
  •  apply the rules for calculating derivatives, both general rules and special rules for the elementary functions.
  •  determine the tangent and normal lines to the graph of a function.
  •  use derivatives to obtain linear approximations.
  •  use the mean-value theorem to evaluate the relevance of the derivative for the increase or decrease of functions, to draw conclusions from the change of sign of the derivative.
  •  use the derivative to solve equations numerically, especially with Newton's method.
  •  use and interpret derivatives of higher order, especially second derivatives and their roles for convexity/concavity.
  •  draw graphs of functions with the aid of first and second derivatives, and then also to find potential asymptotes.
  •  solve applied max-min problems using the derivative.
  •  achieve an understanding of the concept of an integral via area and approximating sums.
  •  interpret the integral as a limit of Riemann sums, and to use this to derive integral formulas, such as the formula for volume by slicing.
  •  understand the mean-value theorem for integrals and the fundamental theorem of calculus.
  •  use techniques (e.g. integration by part, change of variable and partial fraction decomposition) for calculating antiderivatives to certain elementary functions and to compute definit integrals using the fundamental theorem of calculus.
  •  use numerical methods to compute integrals.
  •  be familiar with Matlab, and to apply this in some chosen part of the course.

Content

  •  The concept of a function.
  •  Limits and continuity, theorems about continuous functions
  •  Derivatives and differentiation rules.
  •  Elementary functions and their derivatives
  •  The mean-value theorem
  •  Inverse functions, logarithms and inverse trigonometric functions
  •  Curve construction
  •  Extreme value problems
  •  Numerical equation solving
  •  Sums and integrals
  •  The fundamental theorem of calculus, antiderivatives
  •  Methods of integration
  •  Applications on intergrals: Area and volume
  •  The basics of Matlab

Organisation

Lectures, exercises and computer exercises.

Literature

Information will be given before the start of the course.

Examination including compulsory elements

In order to complete the course, the student have to:
- pass a written exam.
- produce an approved computer exercise.

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 on educational support due to disability.