MM503: Biomath I (5 ECTS)

STADS: 13000301

Level
Bachelor course

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

Teacher responsible
Email: svensson@imada.sdu.dk

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

Comment:
Ubegrænset deltagerantal. Kurset kører i 2. kvartal. Fælles undervisning med MM501.

Prerequisites:
None

Academic preconditions:
Danish high school mathematics (A level).

Course introduction
To supply the students with basic mathematical tools in single-variable calculus and introductory probability theory with a view towards applications in biology.



Qualifications
Based on high school mathematics (B-level), the students will be introduced to and trained in a number of fundamental concepts related to functions of a single variable and introductory probability theory.
The course thus equips the students with basic mathematical tools for further studies in the biological sciences. Having completed the course successfully, the student can be expected to

- have a solid understanding of basic concepts from single-variable calculus, and to be able to apply these in connection with mathematical modelling of biological phenomena.
- be familiar with basic notions from probability theory in preparation for the course in statistics in the fourth quarter.

Expected learning outcome
At the end of the course the student will beable to:

* carry out simple mathematical reductions and differentiation of expressions involving (finite) sums, differneces, products, fractions, powers, roots and logarithms.
*determine the linearization and the second and third orther Taylorpolynomials of a given function at a given point.
*interpret the linearization as a model for the tangent at a given point.
*interpret and apply differentiation as a tool to determine stationary points and image set of a given function.
*evaluate determined and undetermined integrals for powers, logarithmic, exponential and trigonometrical functions.
*interpret determined and undetermined integrals as areas and primitive functions.
*determine the limit of a mathematical expression in one variable as this variable tends to both infinity and a finite value.
*apply the above mentioned techniques in relation to simple modelling problems.
*calculate the mean value, variance and correlation for discrete and continuous stochastic variables.
*determine (conditional) probabilities of given events in finite as well as infinite probability spaces.
*apply conditional probability to determine whether two given events are independent.
*apply the addition and multiplication principles to determine the number of possibilities in given combinatorial problems.
*apply the above mentioned topics to examples in biology.

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.

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 number of mandatory assignments which 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.
b) A three hour written exam with books, notes, etc. Lap top is allowed at the exam. (The lap top can not be loud, and printer is prohibited.) Internal examiner, pass/fail

Re-exam after fourth quarter.

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

(a) Forelæsninger (26 timer).
(b) Eksaminatorier/opgaveregning (24 timer).
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.