Course syllabus for Calculus in one variable

The course syllabus contains changes
See changes

Course syllabus adopted 2019-02-21 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematisk analys i en variabel
  • CodeMVE017
  • Credits7.5 Credits
  • OwnerTKIEK
  • 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 51130
  • 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 2021 am J
  • 07 Apr 2021 pm J
  • 16 Aug 2021 am 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

Introductary course in mathematics.

Aim

The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics required in further studies as well as in the future professional career

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

After completion of the course the student shall

-    Understand and be able to define the concepts definite, indefinite and improper (Riemann)integral, know the basic theorems in this context, be able to prove a selection of them, and use them to solve problems.
-    Independently (without aids) be able to compute fairly complex integrals using knowledge of antiderivatives of some elementary functions, integration by parts, direct and indirect substitutions and decomposition into partial fractions.
-    Independently (without aids) be able to compute the volume of a body using the slice and shell formulas, the area of a surface of revolution and the length of a graph.
-    Understand the idea of a differential equation and its solutions as well as be able to infer such an equation from a verbal description of a simple real-world situation.
-    Independently (without aids) be able to solve linear and separable first order differential equations, and second order linear equations with constant coefficients, homogeneous as well as inhomogeneous.
-    Understand the concepts number sequence and series, their convergence, know basic theorems in this context, be able to prove some of them, and use them when solving problems.
-    Understand the concepts power series, their interval of convergence, Maclaurin- and Taylor series/polynomials of a function, be able to determine them and use them when solving problems.
-    With aid in the form of a table of Maclaurin series be able to use power series to determine limits, sums of series, approximations and solving differential equations.
-    Use the software MATLAB to numerically calculate determined integrals using various methods, with aid be able to infer error estimates of the results, as well as numerically solving first and second order differential equations using Euler¿s method and native commands.

Content

- Definition and properties of determined and improper integrals.
- Antiderivatives and their relation to determined integrals.
- Methods for determining antiderivatives; knowledge of antiderivatives of some elementary functions, direct and indirect substitution, integration by parts and decomposition into partial fractions.
- Numerical calculations and error estimates of integrals using the Trapezoidal, Midpoint and Simpson¿s rules and commands native to the software MATLAB.
- Computation of volumes of bodies, area of surfaces and length of graphs using integrals of functions of one real variable.
- First order linear and separable differential equations, second order linear equations with constant coefficients. Basic modelling in connection with this.
- Number sequences, series and criteria for their convergence.
- Power series and their basic properties, Maclaurin and Taylor series/polynomials of functions.
- Using power series to determine limits, sums of series, approximations and solving differential equations.

Organisation

Instruction is given in lectures, classes and laboratory sessions. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

More detailed information of the examination will be given on the course web page before start of the course. Examples of assessments are:

- selected exercises presented to the teacher orally or in writing during the course,
- optional assessments that can give bonus points,
- written or oral exam at the end of the course.
- exercises solved with software and presented to the teacher at the computer.

The course syllabus contains changes

  • Changes to examination:
    • 2020-09-30: Grade raising No longer grade raising by GRULG