MTH436: Mathematical Analysis and Topology I Spring 2018 | |

General Information Course Goals Course Schedule Assignments |
## Course TopicsHere are (some of) the topics that will be covered in this class. ## Continuity- Uniform Continuity
- Monotone Functions
## Differentiation- Definition of the derivative
- Mean Value Theorem
- Taylor's Theorem
- L'Hospital's Rule
## Riemann Integral- Definition
- Integrable and non-integrable functions
- Fundamental Theorem of Calculus
## Sequences of Functions- Pointwise and Uniform Convergence
- Convergence Tests
- Properties of Uniform Limits
- Series of Functions
## Metric Spaces- Continuity
- Compactness
## Optional Further Topicse.g Vector Analysis, definition of a derivative in several variables, more metic spaces/basic topology, generalised Riemann Integral,...## Course GoalsBy the end of the course, you should be comfortable with all the standard material of Real Analysis: sequences, continuity, derivatives and integrals. You should also have a basic understanding of metric spaces and how they generalise the notions of real analysis. |