Syllabus for |
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| TMV130 - Calculus in one variable |
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| Syllabus adopted 2011-02-22 by Head of Programme (or corresponding) |
| Owner: TKVOV |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: First-cycle |
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Major subject: Architecture and Engineering, Mathematics, Civil and Environmental Engineering
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: Swedish
Block schedule:
LA
| Course module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0104 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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18 Dec 2013 am V, |
25 Apr 2014 am V, |
29 Aug 2014 am V |
In programs
TKVOV CIVIL ENGINEERING, Year 1 (compulsory)
TKATK ARCHITECTURE AND ENGINEERING, Year 1 (compulsory)
Examiner:
Docent
Johan Karlsson
Course evaluation:
http://document.chalmers.se/doc/05a47662-1a51-418b-a30c-505590375ce3
Go to Course Homepage
Eligibility:
For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
Course specific prerequisites
Introductory 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 this course the student should
-have deepened knowledge of elementary functions.
- have attained good knowledge about the integral and its relation to differentiation.
- be acquainted to both analytical and numerical methods for calculating integrals.
- have a good understanding of the meaning of an ordinary differential equation.
- be familiar with both analytical and numerical methods for solving ordinary differential equations.
- be familiar with how functions can be approximated by polynomials and represented by power series.
- be able to use and combine different concepts in problem solving.
- be able to use the software MATLAB in problem solving.
Content
Anti-derivatives and integrals, methods of integration.
Improper integrals.
Applications of integration: Area, volume, centre of mass, arc length,
area and volume of solids of revolution
Introduction to numerical analysis, computer arithmetic.
Numerical integration: the trapezoid rule, Simpson's rule.
Taylor's formula, series and power series.
Theory of algebraic equations with complex coefficients.
Ordinary differential equations: First-order equation in general,
analytical solution of separable and linear equations. Second-order
linear equations with constant coefficients, the equations of simple and
damped harmonic motion. Higher-order linear equations with constant
coefficients. Change of variables in ordinary differential equations.
Numerical derivatives and numerical solution of ordinary differential
equations.
Introduction to MATLAB, programming and applications.
Organisation
Instruction is given in lectures and classes. 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
More detailed information about the examination will be given on the
course web page before start of the course.
Examples of assessments are:
-selected exercises are to be presented to the teacher orally or in
writing during the course,
-other documentation of how the student's knowledge develops,
-project work, individually or in group,
-written or oral exam during and/or at the end of the course.