MM536: Calculus for mathematics
Internal Course Code
Comment
Entry requirements
Academic preconditions
Course introduction
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
Examination regulations
Exam element a)
Timing
Tests
Mandatory assignment
EKA
Assessment
Grading
Identification
Language
Examination aids
To be announced during the course
ECTS value
Additional information
Exam element b)
Timing
Tests
Written examination
EKA
Assessment
Grading
Identification
Language
Duration
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
Additional information
Indicative number of lessons
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.