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Home>Study Programmes>Bachelor in Applied Computer Science>Courses>Analysis - 2009/2010 - Computer Science
COURSE PRESENTATION FORM - ANALYSIS - 2009/2010


COURSE NAME: Analysis

COURSE CODE: 70135 (BSc) / 70007 (BSc Old)

LECTURER: Ricardo Alberto Marques Pereira

TEACHING ASSISTANTS:  Ricardo Alberto Marques Pereira (EN), Lucia Bertoluzza (IT), Andrea Janes (DE) 

TEACHING LANGUAGE: English

CREDIT POINTS: 8 (BSc) / 6 (BSc Old)

LECTURE HOURS: 48

EXERCISE HOURS: 24

TIMESPAN: 28.09.2009 - 23.01.2010

TIMETABLE: see Timetable Page

OFFICE HOURS LECTURER: Friday 14:40 - 17:20, Faculty of CS, Piazza Università, office C5.01

OFFICE HOURS TEACHING ASSISTANTS:
Ricardo Alberto Marques Pereira: same as for the lecture;
Lucia Bertoluzza: Thursday 16:00 - 17:20, Faculty of CS, Piazza Università, office C5.01;
Andrea Janes: to be determined.


PREREQUISITES
Elementary notions of:
set theory, logic, algebra (linear and quadratic equalities and inequalities), powers and radicals, exponentials and logarithms, trigonometry, geometry (points and vectors in one and two dimensions) and the Cartesian plane (straight line and parabola).

OBJECTIVES
Introduction to the theory of functions of one real variable:
domains and graphs, elementary functions, limits, continuity, differentiation, polynomial approximations (Taylor’s formula), optimization (maxima and minima), convexity and concavity, graphs of functions, integration, techniques of integration, sequences and series, linear differential equations.

SYLLABUS
  • The real line R: intervals, metric, and topology.
  • Real variable functions: positive/negative domains, graphs.
  • Linear and quadratic functions and their graphs.
  • Elementary functions and their graphs.
  • Limits at a point and limits at infinity.
  • Continuity and theorems on continuity.
  • Differentiation: derivatives, rules of differentiation.
  • Theorems on differentiation.
  • Polynomial approximations and Taylor’s formula.
  • Limits revisited: indeterminate forms and l’Hospital’s rule.
  • Optimization in one variable, local minima and maxima.
  • Convex and concave functions, global minima and maxima.
  • Sketching the graph of functions.
  • Integration: definite and indefinite integrals, rules of integration.
  • Theorems on integration, the fundamental theorem of calculus.
  • Integration by substitution and integration by parts.
  • Improper integrals, convergence and divergence.
  • Sequences and convergence.
  • Series and convergence.
  • Taylor and Maclaurin series.
  • First order linear differential equations.
  • Second order linear differential equations.

The 6 credit points exam regards all subjects except Sequences and Series plus First and Second Order Linear Differential Equations.


TEACHING FORMAT
Classical classroom lectures for both theory and exercise classes.

ASSESSMENT
The assessment is based on one midterm exam and one final exam (which can be taken in June/July, September, or January/February).
All exams are written exams.
The assessment scheme is as follows:
Exams are rated from 0 to 30 and (as usual) the ‘sufficiency’ level (minimum pass mark) is 18.
If the midterm mark is sufficient, then the course mark is given by the average between the midterm and final marks. Otherwise, the course mark is simply the final mark.
The students with sufficient midterm mark can choose between a final on the full program of the course OR a final only on the second half of the course program.

READING LIST
Textbook:
  • Robert A. Adams: Single variable calculus (3rd ed.), Addison Wesley 1995, or Calculus of one variable (5th ed.), Addison Wesley 2003.

SOFTWARE USED
None.

LEARNING OUTCOME
Basic concepts and techniques of single variable differential calculus: limits, derivatives, integrals, sequences and series, first and second order linear differential equations.

COURSE PAGE
For didactic reasons no materials are available on-line: students have to use the textbook.




Credits
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