MM501: Calculus I (5 ECTS)

STADS: 13000101

Level
Bachelor course

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

Teacher responsible
Email: swann@imada.sdu.dk

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

Comment:
31.10.2006:Skemaændringer S14.

Prerequisites:
None

Academic preconditions:
Danish high school mathematics (high level) must be passed.

Course introduction
To prepare the students for the fundamental applications of mathematics in the natural and technical sciences and for further studies in mathematics.

Qualifications
Based on high school mathematics (high level), the students will be introduced to and trained in a number of fundamental concepts related to functions of a single variable. 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 single-variable calculus to establish, solve and interpret mathematical models in the natural and technical sciences.

- produce, formulate and carry out basic mathematical reasoning in connection with given problems of mathematical nature.

- be familiar with basic notions from probability theory in preparation for the course in statistics in the fourth quarter.

Expected learning outcome


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

• 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 textbook, notes, etc. Lap top is allowed at the exam. (The lap top can not be loud, and printer is prohibited.)
(b) A written project in mathematics.
(c) A number of mandatory assignments during the course.
The mandatory assignments 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. The remaining 4 ECTS are evaluated through the written exam (80%) and the project (20%). Based on the exam and the project the student is assigned the grade pass/fail (internal examiner by teacher). Re-exam after third quarter.

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 timers ugentlige opgavelaboratorier, hvor de studerende opdelt i ’store’ hold kan regne opgaver under vejledning af instruktorer.
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.