MM01: Calculus (12 ECTS)

STADS: 1301801

Level


Teaching period

Autumn and spring semesters (one year course).

Teacher responsible
No responsible teachers found, contact the department if necessary

Timetable
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Comment:
6 ECTS ud af 12 ECTS, fortsat fra sidste semester.

Prerequisites:
None

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

Course introduction
To prepare the students for the fundamental applications of mathematics in the sciences and for a further study of mathematics.

Expected learning outcome


Subject overview
Differentiation and integration of the standard functions, including hyperbolic and inverse trigonometric functions. Taylors approximation of degree n for a function of one variable, lHospitals rule. Solutions of first and second order linear ordinary differential equations and methods for nonlinear first order equations. Complex numbers, the complex exponential function and the complex quadratic equation. Infinite series and power series, radius of convergence, representation of functions by power series and applications to solving differential equations. Vectors and matrices, linear transformations of n-dimensional coordinate space. The Jacobi matrix for a vector-valued function of several variables, Taylors formula in two variables and the classification of stationary points. Line integrals of vector fields and the existence of potential functions. Multiple integrals, surface integrals and the flow of a vector field through a surface. The theorems of Green, Stokes and Gauss and applications to calculations of line, surface, and volume integrals.

As an experiment, 3 projects will be part of the course, 2 projects will be assigned in the autumn semester and one in the spring semester. These projects will be carried out jointly with Physics A (FY01) and aim at developing the students ability to use mathematical concepts in physics. They will be carried out in groups of 2 or 3 students and will be evaluated according to the 13-point marking scale. (Students of mathematics and economics will have other assignments in the project period.)

Literature

Robert A. Adams: Calculus, a complete course. 5th Ed., Addison Wesley, 2002

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
A four hour written examination with textbook, notes, etc. External examiner. Marks according to the 13-point marking scale. Mandatory assignments (pass/fail, internal examiner) which accounts for 3 ECTS credits of the 12 ECTS credits. It is not required that these assignments be approved in order to take the examination, but they must be approved in order to obtain the bachelor degree.

Marks for the three projects will weigh 30% in the final marking in Physics A (FY01) and Mathematics A (MM01). The written examination mark will weigh 70%. There is no minimum mark required for the projects. These marks are only valid for the examinations in June and August the same year. Students who do not pass the August examination must repeat the entire course. For students enrolling on 1 September 2003 or later the last January examination will be held in January 2004. Possible applications of exemption must be forwarded to the Study Committee. (For students of mathematics and economics the final examination will weigh 100%.)

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

Forelæsninger (60 timer) og eksaminatorier (60 timer).
Educational activities

Language
This course is taught in Danish.

Remarks
Please remember to register for evaluation of assignments as well as for the written examination.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.