Calculus (CAL)

It is quite possible that computer engineers will encounter problems that involve making calculations at some point in their professional careers. Despite the fact that IT experts do not have to make these sorts of calculations-but rather have them done for them-they still need to be able to implement them. For this reason it is useful for them to understand these calculations and to know where to look for relevant information. In some subjects in this course, students have to know how to perform certain calculations without starting from square one. Thus, the overall goal of the subject is that students in information technology come away with an understanding and ability to work with the fundamental concepts and techniques of mathematics. In particular, the subject aims for students to understand and be able to use the concept of functions with one or more variables.

Knowledges

1. Learn the properties and graphic representation of elementary functions.
2. Learn the basic concepts underlying the integration of the functions of a variable: geometric interpretation, calculation of integrals and improper integrals.
3. Learn the basic concepts underlying successions and numeric series: concept of limit, convergence criteria, techniques for calculating the limits of successions, the concept of sum, convergence criteria and techniques for (exact and appropriate) summing of convergent series.
4. Learn the approximation provided by Taylor"s Polynomial and how to use it.
5. Learn the basic concepts underlying the functions of various variables: special sets, differentiation and application of differentiation and calculating extremes.

Abilities

1. Understand the pass to limit concept.
2. Understand the concepts of exact value, approximate value, and error estimation.
3. Ability to analyze the local behaviour of a variable"s function.
4. Ability to geometrically interpret the functions of diverse variables.
5. Improve algebraic manipulation skills.
6. Understand arguments employing contradiction and ratio ad absurdum.
7. Ability to intelligently use examples and counter-examples.
8. Ability to bear in mind physical and/or geometric versions of the main definitions and results.

Competences

1. Ability to understand problems: given a problem, distinguish between data (or starting elements), unknowns (or what is asked for), hypotheses, and the laws applicable.
2. Ability to think in abstract terms. Ability to tackle new problems by consciously using strategies that have proved useful in solving previous problems.
3. Ability to apply mathematical knowledge and logic in solving problems.
4. Ability to act independently: Know how to work on one"s own with just the bare minimum of knowledge and guidance.
5. Develop recourse to physical or geometric interpretations, or computer use to solve problems of a mathematical nature.
6. Ability to organise one's work: ability to set priorities for various tasks, plan one's time, and organise one's notes.
7. Ability to study various sources, recognise that the information obtained in class is insufficient, and to seek the supplementary information required.
8. Ability to work effectively in small groups to solve problems of middling difficulty.
9. Ability to effectively convey one"s ideas in writing.
10. Assume responsibility for one"s own work.

Theory classes; these consist of the presentation of concepts, and the most basic Calculus techniques and methods.







Classes of problems; these expand on the examples covered in the theory classes and with the solution of problems.







Lab classes; the methods and techniques learnt in the theory classes will be applied to various problems with the aid of the Maple symbolic manipulator.

The final grade (N) for the course is calculated as follows:

N = max( 0.15*L + 0.25*P + 0.6*F, 0.15*L + 0.85*F )

where

L = Lab grade.
P = Part exam grade.
F = Final exam grade.

Lab: average grade from 5 practical sessions, assessed using a questionnaire submitted at the end of each session (15%).

Part exam: This consists of exercises and/or brief questions on theory (25%).

Final exam: This consists of a certain number of problems and/or theoretical questions (60%).

Any attempt of fraud during the course will entail the application of the UPC's general academic normative and the beginning of a disciplinary process.

• Lubary, J.A.; Brunat, J.M. Cálculo para Ingeniería Informática, Temes Clau 8, Ed. UPC, 2008.
• Gerald L. Bradley, Karl J. Smith Cálculo, Prentice Hall, 1998.
• Grau, M. Lliçons de reforç de càlcul., Edicions UPC (Edicions Virtuals), 2000.
• Miquel Noguera Batlle, Miquel Grau Sànchez Anàlisi matemàtica : pràctiques amb Maple V, Edicions UPC, 1996.
• Demidovich, B. et al. Problemas y ejercicios de análisis matemático, Ed. Paraninfo, 1988.
• Antonio Magaña Nieto, José Antonio Lubary Martínez Càlcul I : problemes resolts, Edicions UPC, 1994.
• José Antonio Lubary Martínez, Antonio Magaña Nieto Càlcul II : problemes resolts, Edicions UPC, 1995.

• Alfonsa García López ... [et al.] Cálculo I : teoría y problemas de análisis matemático en una variable, Clagsa, 1994.
• Alfonsa García López ... [et al.] Cálculo II : teoría y problemas de funciones de varias variables, Clagsa, 2002.
• Robert G. Bartle, Donald R. Sherbert Introducción al análisis matemático de una variable, Limusa, 1996.
• G. Baranenkov... [et al.] Problemas y ejercicios de análisis matemático, Paraninfo, 1993.

1. http://www-ma2.upc.es/m2/
   

Knowledge of integers and the properties of operations.
Operating with polynomials: addition, multiplication, division, factoring.
Have a basic grasp of the concept of function.
Know how to operate with exponential functions, logarithmic functions, and trigonometric functions.
The concept of continuous functions. Know how to calculate the limits of functions.
Understand the concept of derivable function. Know how to calculate the derivatives of functions.
The concept of an integral. Know how to calculate integrals.