- Docente: Piero Mazzarisi
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Economics and Finance (cod. 8835)
Learning outcomes
The main aim of the Crash Course in Mathematics is to provide students with the basic contents and instruments required for the Course of Calculus and Linear Algebra.
The arguments of the Crash Course are preparatory for the Course of Calculus and Linear Algebra and will not be repeated later. For this reason attendance is strongly recommended.
Course contents
1. Set of Natural (N), Integer (Z), Rational (Q), Real (R) numbers. Complex (C) numbers.
2. Basic operations and order of operations. Factorisation of an algebraic expression. Product of a sum and a difference. Square of a binomial. Cube of a binomial.
3. Exponential, logarithmic, radical expressions.
4. Polynomials. Algebraic fractions.
5. Linear and quadratic equations. Quadratic formula and other methods to solve a quadratic equation. Geometric interpretation. Higher order equations, absolute value and radical equations.
6. Linear and quadratic inequalities. Systems of inequalities. Radical, absolute value and rational inequalities.
7. Intervals of real numbers. Functions of a real variable: domain, codomain, symmetries, monotonicity, convexity. Inverse functions.
8. Elementary functions: power, radical, exponential and logarithmic functions. Graphs of elementary functions.
9. Graphs of functions of a real variable.
10. Trigonometry. Trigonometric functions and trigonometric identities.
11. Notions of Euclidean geometry. Cartesian coordinates. Fundamental formulas in geometry. Lines. Conic sections: circle, ellipse, parabola, hyperbola.
12. Elementary set theory.
Readings/Bibliography
- Any book of Precalculus, for instance:
"Essential of Precalculus" by Richard N. Aufmann and Richard D. Nation, 1st Edition, Cengage Learning, 2005.
"Essential Mathematics for Economic Analysis" by Knut Sydsaeter, Peter Hammond and Arne Strom, 4th Edition, Pearson 2012
- Precalculus lectures at iLectureOnline(Precalculus)
- Notes on Precalculus (batmath.it)
Teaching methods
Traditional lectures. Exercises.
Teaching tools
Blackboard.
Office hours
See the website of Piero Mazzarisi