Checking date: 07/07/2022

Course: 2022/2023

Calculus I
Study: Dual Bachelor in Engineering Physics and Industrial Technologies Engineering (370)

Coordinating teacher: LLEDO MACAU, FERNANDO

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

By the end of this content area, students will be able to have: 1. Knowledge and understanding of the mathematical principles underlying their branch of engineering. 2. The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems using established methods. 3. The ability to select and use appropriate tools and methods to solve mathematical problems. 4. The ability to combine theory and practice to solve mathematical problems. 5. The ability to understanding of mathematical methods and procedures, their area of application and their limitations.
Skills and learning outcomes
Description of contents: programme
Part I: Real Numbers and Functions Chapter 1: The Real Line 1.1 Ordered Fields 1.2 Number Systems 1.3 Absolute value, bounds, and intervals Chapter 4: Real Functions 2.1 Definition and basic concepts 2.2 Elementary functions 2.3 Operations with functions Part II: Sequences and Series Chapter 3: Sequences 3.1 Sequences of real numbers 3.2 Limit of a sequence 3.3 Number e 3.4 Indeterminacies 3.5 Asymptotic comparison of sequences Chapter 4: Series 4.1 Series of real numbers 4.2 Series of nonnegative terms 4.3 Alternating series 4.4 Telescopic series Part III: Differential Calculus Chapter 5: Limit of a Function 5.1 Concept and definition 5.2 Algebraic properties 5.3 Asymptotic comparison of functions Chapter 6: Continuity 6.1 Definition, properties, and continuity of elementary functions 6.2 Discontinuities 6.3 Continuous functions in closed intervals Chapter 7: Derivatives 7.1 Concept and definition 7.2 Algebraic properties 7.3 Derivatives and local behaviour Chapter 8: Taylor expansions 8.1 Asymptotic comparison of functions 8.2 Taylor¿s polynomial 8.3 Calculating limits 8.4 Remainder and Taylor¿s theorem 8.5 Taylor series 8.6 Numerical approximations 8.7 Local behaviour of functions 8.8 Function graphing Part IV: Integral Calculus Chapter 9: Primitives 9.1 Integration by parts 9.2 Primitives of rational functions 9.3 Change of variable Chapter 10: Fundamental Theorem of Calculus 10.1 Riemann¿s integral 10.2 Properties of the integral 10.3 Riemann¿s sums 10.4 Fundamental theorem of calculus Chapter 11: Geometric Applications of Integrals 11.1 Area of flat figures 11.2 Area of flat figures in polar coordinates 11.3 Volumes 11.4 Length of curves Chapter 12: Improper Integrals 12.1 Improper integrals of the first kind 12.2 Improper integrals of the second kind
Learning activities and methodology
The methodology will be the usual one for classes in the classroom, writing on the blackboard, with the occasional help of some resources on-line to illustrate some graphic or computational aspects of the course. Also, the classroom notes will be uploaded in Aula Global at the end of each chapter, along with the problem sheets that will be solved and discussed in the small groups.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Calendar of Continuous assessment
Basic Bibliography
  • Adrian Banner. The Calculus Lifesaver: All the tools you need to excel at calculus. Princeton University Press. 2007
  • H. Anton, I.C. Bevis & S. Davis. Calculus: Early Transcendentals Single Variable. Wiley. 2008
  • J. Stewart. Single variable calculus: early transcendentals. Brooks-Cole. 1999
  • R. Larson, R.P. Hostetler & B.H. Edwards. Calculus. Brooks-Cole. 2005
  • S.L. Salas, G.J. Etgen & E. Hille. Calculus: One and Several Variables. Wiley. 2006
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • T.M. Apostol. Calculus vol. 1. Wiley. 1991
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus may change due academic events or other reasons.

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