MM502: Calculus II (5 ECTS)

STADS: 13000201

Level
Bachelor course

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

Teacher responsible
Email: swann@imada.sdu.dk

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

Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM504.

Prerequisites:
None

Academic preconditions:
The student must be know with the material of MM501 Calculus I, as well as Danish high school mathematics (high level).

Course introduction
To supply the students with basic mathematical skills based on functions of several variables and infinite sequences and series. In addition, to prepare the students for further studies in mathematics.

Competencies:
Based on the course Calculus I as well as high school mathematics (high level), the students will be introduced to and trained in a number of fundamental concepts related to functions of several variables.
The course thus equips the students with basic mathematical tools for further studies in the Natural and Technical Sciences. Having completed the course successfully, the student can be expected to

- apply the calculus of several variables calculus to establish, solve and interpret mathematical models in the natural and technical sciences.

- 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.

- understand the necessity for further accuracy in the treatment of key notions from the course in order to deal with these in a fully satisfactory way from particularly integrals and infinite sequences and series.

Expected learning outcome
By the end of the course the students will be able to:

- 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.

Syllabus
See syllabus.

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 project assignment. The evaluation accounts for 20% of the final grade for the course.

(c) 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.

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.