MM536: Calculus for mathematics
Study Board of Science
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: 02-03-2023
Duration: 1 semester
Version: Approved - active
Comment
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
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.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give skills to use the appropriate mathematical reasoning and technical terms; analyze and evaluate the theoretical and practical problems for the application of a suitable mathematical model; communicate using a proper mathematical language in writing and orally
- Give knowledge and understanding of basic concepts, theory and methods of mathematics; to conduct analyses using mathematical methods and critically evaluate scientific theories and models.
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
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
Teaching Method
The teaching method is based on three phase model.
- Intro phase (lectures) 56 hours
- Skills training phase: 30 hours, including tutorials: 30
- Study phase. 30 hours
Activities during the study phase:
- preparation of exercises in study groups
- critical discussion of the concepts presented during the lectures.
Teacher responsible
Additional teachers
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
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.