MM536: Calculus for mathematics

Study Board for Natural Sciences

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300059122, N300059102
Assessment: Second examiner: Internal
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N300059101
ECTS value: 10

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Approved - active

Internal Course Code

MM536

Comment

The course is co-read with MM558 from week 43.

Entry requirements

The course cannot be chosen if you have passed, registered, or have followed AI503, MM554, MM556, MM558, FT501 or KE551, or if AI503, MM554, MM556, MM558, MM572, FT501 or KE551 is a constituent part of your Curriculum.

Academic preconditions

Knowledge and skills corresponding to A-level in mathematics from the Danish ‘gymnasium’.

Course introduction

The course will train the students in fundamental concepts and methods within mathematical analysis, including mathematical symbolic language and logical arguments.
The course gives an academic basis for studying the topics of mathematical and numerical analysis (MM533, MM548, MM549), the theory of ordinary and partial differential equations (MM547, MM546), statistics (ST521, ST522) that are part of the degrees of mathematics and applied mathematics.

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:

  • Apply methods and results from calculus to analyze and explain concrete mathematical problems presented during the course.
  • Formulate and, using a mathematical symbolic language, carry out arguments relating to mathematical problems within the syllabus of the course.
  • Solve mathematical problems within the syllabus of the course.

Content

The following main topics are contained in the course:

  • The concept of a function.
  • Real and complex numbers.
  • Supremum and infimum for subsets of the real numbers.
  • Limits of sequences of real numbers.
  • Cauchy sequences and completeness.
  • The Bolzano-Weierstrass theorem.
  • Convergence of monotone and bounded sequences.
  • Limits of series of real numbers.
  • The mean value theorem.
  • Taylor's theorem.
  • The fundamental theorem of analysis.
  • Limits of functions of one and several variables. 
  • Limits of sequences in Euclidean spaces.
  • Continuity of functions of of one and several variables.
  • Differentiation of functions of one and several variables.
  • Integration of functions of one and several variables.
  • Basic differential equations.

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Mandatory assignment

EKA

N300059122

Assessment

Second examiner: Internal

Grading

Pass/Fail

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Additional information

Reexamination is changed to a oral examination of 10 or fewer students registered

Exam element b)

Timing

January

Tests

Written examination

EKA

N300059102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Student Identification Card - Exam number

Language

Normally, the same as teaching language

Duration

3 hours

Examination aids

All common aids are allowed e.g. books, notes and computer programmes which do not use internet etc. 

Internet is not allowed during the exam. However, you may visit the course site in itslearning to open system "DE-Digital Exam". If you wish to use course materials from itslearning, you must download the materials to your computer no later than day before the exam. During the exam you cannot be sure that all course materials is accessible in itslearning.    

ECTS value

5

Additional information

Reexamination is changed to a oral examination of 10 or fewer students registered

Indicative number of lessons

84 hours per semester

Teaching Method

Planned lessons: 

Total number of planned lessons: 84

Hereof: 

Common lessons in auditorium: 56

Exercise classes in classroom: 28

Classical lectures where the lecturer explains the main parts of the teaching material to the students. This process is carried out while paying particular attention to the active participation of the students.

The lectures are supplied by exercise sessions under the supervision of a teaching assistant. In these sessions, the students are supposed to work with and present exercises related to the material covered in the lectures.


Other planned teaching activities:

  • Reading and understanding of textbook material as preparation for the lectures, either individually or in study groups.
  • Critical discussion of the concepts presented during the lectures.
  • Preparation of exercises ahead of the exercise sessions, either individually or in study groups.
  • Preparation of mandatory assignments.

Teacher responsible

Name E-mail Department
Jens Kaad kaad@imada.sdu.dk Analyse

Additional teachers

Name E-mail Department City
Jens Kaad kaad@imada.sdu.dk Analyse

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.