Mathematical analysis [Matricole dispari]
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Primo semestre dal Oct 3, 2022 al Jan 27, 2023.
The course provides the students with the fundamental notions of differential and integral calculus and the foundations of the symbolic logic and discrete mathematics. The students will be able to: analyze and model problems rigorously; apply effectively mathematical-logical techniques (deduction, induction, function optimization, asymptotic analysis, elementary com-binatorics); evaluate the correctness of logical arguments and identify mistakes in deductive processes.
Prerequisites and basic notions
- Sets and functions, elementary algebra, solving equations and inequalities (and systems of equations and inequalities) of first and second degree.
- Geometric properties of the main plane figures and solid shapes.
- Representating geometric figures in the Cartesian plane.
- Basics of trigonometry.
- Power and root functions, absolute value function.
- Exponential function, logarithm and their graphs.
- Trigonometric functions and their graphs.
- Solving simple equations and inequalities that contain the functions above.
- Representing data, relations and functions with formulas, tables, bar charts and other graphical representations.
- Logical deductions of moderate complexity and logical implications between elementary sentences.
Preliminaries: mathematical induction, properties of the real numbers, real-valued functions of a real variable.
Limits. Continuous functions of a real variable.
Differentiable functions of a real variable.
Integrals (of continuous functions).
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Learning assessment procedures
The exam consists of a written text only. It contains both exercises (for instance, computing limits, derivatives and integrals, studying the properties of a function of a real variable and plotting its graph, deciding whether a given series is convergent or not...) and theoretical questions (stating a definition or a result from the syllabus, proving simple statements that were not covered in class).