MM501: Calculus I (5 ECTS)

STADS: 13000101

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
First quarter.

Teacher responsible
Email: swann@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal, dog højst 30 studerende pr. hold for eksaminatorierne

C står for LektieCafe!

Prerequisites:
None

Academic preconditions:
Danish high school mathematics (high level) must be passed.

Course introduction
To prepare the students for the fundamental applications of mathematics in the natural and technical sciences and for further studies in mathematics.

Expected learning outcome
At the end of the course the student should be able to

* apply methods and results of differentiation and integration for functions of one variable to solve mathematical problems with in the
scope of the course syllabus, including mathematical models used in science;
* compute mean, variance and standard deviation for a random variable with a given probability density function;
* decide whether a given function is a probablity density function, and fit parameters so a given function becomes a probability density function;
* solve simple algebraic equations in one complex variable, do simple arithmetic operations on complex numbers and convert between rectangular and polar representations of a complex number;
* present, formulate and carry out basic mathematical arguments needed for mathematical problems for the above topics

Subject overview
1) Differentiation and integration of standard funktions (including logarithms, exponentials and power functions, the hyperbolic functions, the inverse trigonometric functions and rational functions.
2) The mean value theorem, Taylor polynomials for functions of a single variable, estimation of the error term in Taylor approximations, l'Hopital's rules for calculating limits.
3) Linear differential equations of first and second order and separable first order differential equations (solution methods and applications).
4) Riemann sums, the Riemann integral, The Fundamental Theorem of Calculus.
5) Probability theory: Random variables, density functions, mean, variance and standard deviation, the Gaussian distribution.
6) Complex numbers, the n roots of unity, the complex exponential function, the complex quadratic equation.
7) Functions of several variables and their partial derivatives.

Literature

Meddeles ved kursets start.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
(a) A two hour written exam with textbook, notes, etc. Lap top is allowed at the exam. (The lap top can not be loud, and printer is prohibited.)
(b) A written project in mathematics. The written project can be reused for the re-exam after the second quarter, but can not be used for re-exams at later dates.
(c) A number of mandatory assignments during the course. The mandatory assignments account for 1 ECTS of the total 5 ECTS of the course (pass/fail, internal examiner). These assignments are not part of the first year test. The remaining 4 ECTS are evaluated through the written exam (80%) and the project (20%). Based on the exam and the project the student is assigned the grade pass/fail (internal examiner by teacher). Re-exam after third quarter.

Re-exam after second quarter.

Expected working hours
The teaching method is based on three phase model.

(a) Forelæsninger (26 timer).
(b) Eksaminatorier/opgaveregning (24 timer).
(c) 4 timers ugentlige opgavelaboratorier (lektiecafé), hvor de studerende har mulighed for at regne opgaver under vejledning af instruktorer.
Educational activities

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.