Mathematics pre-course

UNIVERSITÀ DEGLI STUDI DI PAVIA
Department of Economics and Management
in collaboration with
the Department of Mathematics and the Department of Physics

MATHEMATICS PRE-COURSE FOR REAL ANALYSIS

The precourse is highly recommended for everyone, especially for those without a solid background in calculus (derivatives and integrals) or algebra (solving equations and inequalities).

The content of the precourse is necessary in order to follow the course and it may be tested at the oral examination.

1. Course content.

Basic Functions of one variable (powers, polynomials, rational functions, exp, log, sin, cos)
Equalities - inequalities.
Analytic geometry.
Derivatives (for one-variable functions).
Integration (for one-variable functions).

2. Lecture notes and videos.

Lesson 1 [lecture notes - pdf]

[Video 1] Numerical sets, cardinality.
[Video 2] Cardinality, 2nd and 3rd power of a binomial
[Video 3] nth power of a binomial, powers (rules). Geometry: line and parabola.
[Video 4] Geometry: circumference, ellipse, hyperbola. Functions: domain, codomain, graph.

Lesson 2 [lecture notes - pdf]

[Video 1] Exponential and logarithmic functions. Equations and inequalities: linear and quadratic.
[Video 2] Equations and inequalities: quadratic and higher order.
[Video 3] Equations and inequalities: rational, with roots.

Lesson 3 [lecture notes - pdf]

[Video 1] Equations and inequalities: exponential and logarithmic.
[Video 2] Trigonometric functions and equations.
[Video 3] Trigonometric equations and inequalities. Limits.

Lesson 4 [lecture notes - pdf]

[Video 1] Limits, De l'Hôpital Theorem. Derivatives.
[Video 2] Derivatives: Leibniz rule, chain rule. Application to optimization. Integrals.
[Video 3] Integrals, fundamental theorem of calculus.

3. Additional resources.

This section collects some resources about Calculus, mainly based on the useful MIT Open Courseware. The links lead to the specific course, where you can find videos, textbooks references, and exercises (see, in particular, the 'Assignments', 'Reading material', and 'Related resources' sections). More resources are available at the end of this webpage.

Pre-calculus (EduOpen)
Single variable calculus (MIT Open Courseware)
Textbook: G. F. Simmons, Calculus with analytic geometry. McGraw-Hill, 1996.
Calculus problem list (eCalculus.org)

Instructor:

Professor Marco Veneroni, Dipartimento di Matematica "Felice Casorati", webpage .

Last modified: 31/05/2024