Course
Mathematical Analysis (MAT310)
The course covers fundamentals of mathematical analysis:
Dette er emnebeskrivelsen for studieåret 2015-2016. Merk at det kan komme endringer.
Semesters
Fakta
Emnekode
MAT310
Vekting (stp)
10
Semester undervisningsstart
Autumn
Undervisningsspråk
English
Antall semestre
1
Vurderingssemester
Autumn
Timeplan
Content
Real numbers, topology, continuous functions, sequences and series, uniform convergence, Riemann integral, calculus of variations
Learning outcome
Upon completing this course students should be able to:
- Clearly understand what is meant by mathematical proof, and how to communicate mathematical arguments clearly in the form of a mathematical proof
- Understand the notions of sequence, subsequence and accumulation point. Understand and define the notion of convergence for sequences. Be able to define the notion of function and the notions of continuity and derivative
- Understand the basic ideas in point set topology, particularly openness, closeness, connectedness and compactness, and understand how topological results are used in the proofs of familiar theorems in analysis
- Understand and be able to use the Intermeiate Value Theorem and the Mean Value Theorem. Define the pointwise and uniform convergence of sequences of functions
- Define the Riemann definite integral as a limit of Riemann sum approximations, and be able to formulate and use the Fundamental Theorem of Calculus. Know elementary properties of the Riemann integral and be able to formulate and use the Fundamental Theorem of Calculus
- Formulate some classical variational problems, understand the idea of the classical variational method, and be able to derive and solve the Euler equations for a variety of types of problems.
Forkunnskapskrav
Et av følgende alternativer:
Mathematical Methods 1 (MAT100)
Mathematical Methods 2 (MAT200)
Mathematical Methods 1 (MAT100)
Mathematical Methods 2 (MAT200)
Anbefalte forkunnskaper
Vector Analysis (MAT300)
Exam
| Form of assessment | Weight | Duration | Marks | Aid | Exam system | Withdrawal deadline | Exam date |
|---|---|---|---|---|---|---|---|
| Written exam | 1/1 | 4 Hours | Letter grades | No printed or written materials are allowed. Approved basic calculator allowed | — | 01.11.2015 | 03.12.2015 |
Fagperson(er)
Head of Department:
Bjørn Henrik AuestadCourse coordinator:
Helge Paul RuddatMethod of work
3 hours lectures and 2 hours problem solving per week.
Overlapping
| Emne | Reduksjon (SP) |
|---|---|
| Mathematical Analysis (BMA100_1) , Mathematical Analysis (MAT310_1) | 5 |
Åpent for
Bachelor studies at the Faculty of Science and Technology. Master studies at the Faculty of Science and Technology
Emneevaluering
Form and/or discussion.
Litteratur
Frank Morgan: Real Analysis and Applications, 2005. American Mathematical Society.
The course description is retrieved from FS (Felles studentsystem). Version 1