MM504: BioMath II (5 ECTS)

STADS: 13000401

Level
Bachelor course

Teaching period
The course is offered in the spring semester.
Third quarter on 1. year.

Teacher responsible
Email: kriesell@imada.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Kurset er nedlagt.

Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM502.

Prerequisites:
None

Academic preconditions:
The student must know the material of MM503 BioMath 1 as well as Danish high school mathematics (A level).

Course introduction
To supply the students with basic mathematical skills based on functions of several variables and infinite sequences and series. The topics of the course are treated with a view towards applications in the biological sciences.

Expected learning outcome
- apply methods and results in calculus for functions of several variables to solve mathematics problems within the syllabus of the course
- work analytically with a wide variety of mathematical objects and phenomena in three a dimensional space and to have a visual geometric understanding of the relevant constructions and results studied in that connection
- compute and interpret partial derivatives, the gradient and the directional deriviative of a function in several variables; find and classify critical points of a function in two variables; apply and and interpret the chain rule for functions in several variables; to compute and interpret double and triple integrals
- interpret vector fields, determine field lines, determine when vector fields are conservative, and to determine a potential function for a conservative vector field
- determine when series and sequences converge, and calculate the value of certain series
- formulate and apply basic mathematical reasoning within the topics mentioned above

Subject overview
1. Functions of several variables, partial derivatives, gradients and directional derivatives, the chain rule, Taylor’s formulae for functions of several variables, classification of critical points.

2. Riemann sums, double integrals, calculation by iteration, double integrals in polar coordinates, triple integrals.

3. Line integrals of vector fields and the existence of potential functions. Surface integrals and the flow of a vector field through a surface. The theorems of Green, Stoke and Gauss and applications to calculations of line, surface, and volume integrals.

4. Infinite sequences and series: Sequences, bounded sequences, monotone sequences, convergence/divergence for sequences, infinite series, convergence, divergence and absolute convergence, geometric series, power series, radius of convergence, representation of functions by power series and applications to solving differential equations.

Literature

• Meddeles ved kursets start..

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
(a) 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.) External examiner, grades according to the 7-point marking scale.

Re-exam after fourth quarter. (b) A number of mandatory assignments which account for 1 ECTS of the total 5 ECTS of the course (pass/fail, internal examiner).

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.