Mathematics BSc
Course description
2013.
Course description
2013.
Analysis 1
| Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
|---|---|---|---|---|---|---|
| 3 + 4 | 3 + 5 | exam + term grade |
all | mm1c1an1 mm1c2an1 |
1 | alternative |
Course coordinator
| Strong | Weak | Prerequisites | |
|---|---|---|---|
| Lecture | |||
|
Weak:
practice class
| |||
Remarks
- You have to take exactly one of the following two equivalent sets of courses: {Analysis 1, Analysis 2} or {Calculus 1, Calculus 2, Foundations of analysis}.
Syllabus designed by:
Prerequisites
A thorough understanding of High school mathematics.
Syllabus
- Basic concepts of mathematical logic. Some basic tools for proving theorems. Classical inequalities. Sets, functions sequences.
- Axioms of the real numbers. Models of real numbers. Least upper bound and greatest lower bound. Powers.
- Convergence of sequences. Sequences tending to infinity. Basic properties of convergent sequences. Monotone sequences. The limit superior and limit inferior. The Bolzano-Weierstrass theorem. Cauchy sequences.
- Countable and uncountable sets.
- Convexity and monotonicity of real functions. Limits of functions. Continuous functions. Interior points, cluster points and isolated points.
- Global properties of continuous functions on closed intervals. Monotonic functions and continuous functions. Convex functions and continuous functions.
- Some elementary functions (polynomials, rational functions, trigonometric functions, hyperbolic functions).