MM502: Calculus II (5 ECTS)

STADS: 13000201

Level
Bachelor course

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

Teacher responsible
Email: mikael@imada.sdu.dk

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

Comment:
REGNEØVELSER MANDAGE (U9)og TIRSDAGE (U2)KL.14-17 I ugerne 6-11.

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


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

• Robert A. Adams: Calculus, a complete course, 5th Ed., Addison Wesley, 2003.

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 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. Tha evaluation accounts for 20% of the finally 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 (25 timer).
(b) Eksaminatorier/opgaveregning (25 timer).
(c) Det overvejes på forsøgsbasis at indføre 2-3 ugentlige timers opgavelaboratorier, hvor de studerende opdelt i ’store’ hold kan regne opgaver under vejledning af en VIP.
Educational activities

Language
No recorded information about the language used in the course.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.