| Lectures and exercises |
hours |
| Topics |
Specific contents |
|
| Fundations and numbers |
Real numbers, order and extremes.
Complex numbers and their representation |
12
|
| Sequences and finite difference equations |
Sequences and limits. Properties of limits, indetemined forms
Finite difference equations |
14
|
| Numerical series and series of functions |
Numerical series and convergence criteria.
Sequences of functions, series of functions
Real power series |
10
|
| Limits and continuity |
Topological spaces, in particular metric spaces. Limits and their properties.
Continuity and structure of the space of continuous functions
Connection, compactness and uniformity properties |
6
|
| Differential calculus in one variable |
Derivatives and their operating rules. Differential.
Monotonicity and extrema.
Taylor's formula and De l'Hopital rule
Convexity and global properties |
16
|
| Integral calculus in one variable |
Integral and fundamental theorem of integral calculus
Integration techniques. Improper integral
Line integral and work integral. Exact differentials |
18
|
| Introduction to function theory |
Complex series; holomorphical functions and Cauchy-Riemann equations. Integration in the complex field, calculus of residues and its applications |
12
|
| Differential equations |
Generalities and Cauchy problem
Linear differential equations, homogeneous and non homogeneous
Autonomous equations and separate variables equations |
12
|
| Critical revision |
Stractural analysis of the proofs of some theorems.
Problem solving
Structural decomposition of some complex problems |
14
|
| Total hours for lectures and exercises |
114 |
| for exercises only |
40 |
|
Further educational activities
|
hours
|
| Labs |
24 |
| Tutorials / Seminars |
|
| Workshops |
|
| Guided tours |
|
| |
|
| Total hours for further educational activities |
24 |
| Total hours |
138
|