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Glossary
Semester (Sem)
1First Semester
2Second Semester
AAnnual course
Educational activities
ABasic activities
Language
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
  • Soft Skills
Course Details
Context
Academic Year 2018/2019
School School of Architecture Urban Planning Construction Engineering
Name (Bachelor of Science degree)(ord. 270) - MI (497) Building and Construction Engineering
Track IE1 - Curriculum - IEC
Programme Year 1

Course Details
ID Code 053110
Course Title MATHEMATICAL ANALYSIS 1
Course Type Mono-Disciplinary Course
Credits (CFU / ECTS) 9.0
Semester First Semester
Course Description "1. Sets. Natural, integer, rational numbers. Summation and product symbols. Factorial and binomial coefficients. Newton's formula. Real numbers. Bounded sets, maximum, minimum, upper and lower bounds. Absolute value, distance between real numbers, triangle inequality, neighbourhoods, limit points. Complex numbers, complex plane. Algebraic, polar end exponential forms; operations. Functions: domain, natural domain, codomain, image, graph. Extensions and restrictions. Injective and surjective functions; inverse functions. Extrema of a function. Functions that are: bounded, monotonic, even, odd, periodic. Elementary functions and their graphs. Transformations of sets in the plane and graphs of functions. Composition of functions. Sequences. Limits of functions, basic properties and theorems, indeterminate forms. Particular case of limits of sequences. Special limits. The number e. Landau's symbols, their properties and use for calculations of limits. Continuous functions. Continuity of elementary functions. Discontinuities. Extensions by continuity. Fundamental theorems about continuous functions (Weierstrass, zeroes, intermediate values). Continuity of composed and inverse functions. Asymptotes. Derivative of a function, geometrical meaning, tangent line. Differentiation and continuity. Left and right derivatives, singular points. Derivatives of elementary functions. Differentiation rules. Derivatives of higher order. Stationary points and Fermat's theorem. Some fundamental theorems (Rolle, Lagrange, de l'Hospital). Monotonicity theorems. Taylor's formula. Convexity. Investigation of the main features of a function and sketch of its graph. Antiderivative and indefinite integral; methods for finding integrals. Definite integral and properties. Integrability of continuous functions. Mean value and mean value theorem. Functions defined by integrals. Fundamental theorems of calculus. Improper integrals: definitions and criteria for the study of convergence. Regular curves. Differential calculus for curves. Rectifiable curves, length. The arc-length parameter. Line integrals and applications. Series of numbers: convergent, divergent, oscillating. Some special series. Criteria for convergence and divergence. Hints at approximate determination of sums of convergent series."
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU
A
MAT/05
MATHEMATICAL ANALYSIS
9.0
Innovative teaching The course includes  1.0  credits in Innovative Teaching as follows:
  • Blended Learning & Flipped Classroom

Schedule, add and removeAlphabetical groupProfessorLanguageCourse details
From (included)To (excluded)
--AZZZZDi Cristo Michele
manifesti v. 3.2.3 / 3.2.3
Area Servizi ICT
21/02/2020