Checking date: 07/07/2020

Course: 2020/2021

Differential Calculus
Study: Bachelor in Applied Mathematics and Computing (362)

Coordinating teacher: ROMERA COLMENAREJO, ELENA

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

Students are expected to have completed
Acquire and manage the mathematical language that allows the student to understand, formulate and solve problems that arise in computation and engineering. Get familiar with the functions of one real variable, their properties of continuity, differentiability and graphic representation with their applications. Understand and be able to manage the formal language of demonstrations of the mathematical results. Manage sequences and series of real numbers and of functions, understanding the different kinds of convergence.
Description of contents: programme
1. Real variable functions 1.1 The real line: sets of numbers, properties, absolute values 1.2 Elementary functions and curves 1.3 Polar coordinates 2. Limits and continuity 2.1 Limits of functions. Properties and fundamental theorems 2.2 Continuity of functions. Fundamental theorems 2.3 Uniform continuity 3. Derivatives and their applications 3.1 Definition, properties, derivatives of elementary functions 3.2 Meaning of the derivative. Extrema 4 Local study of a function 4.1 Graphic representation 4.2 Taylor's polynomial and its applications 5. Sequences and series of real numbers 5.1 Sequences of numbers. 5.2 Series of positive numbers 5.3 Absolute and conditional convergence 6. Sequences and series of functions 6.1 Sequences of functions. Punctual and uniform convergence 6.2 Series of functions. Punctual and uniform convergence 6.3 Taylor series
Learning activities and methodology
1. MASTER CLASSES: Development of the theoretic part of the matter 2. PROBLEMS CLASSES: Resolution of problems and exercises in participatory classes 3. TUTORIES: Personal or group assessment for the students 4. SELF-EVALUATIONS: Control of the evolution of the student
Assessment System
  • % end-of-term-examination 50
  • % of continuous assessment (assigments, laboratory, practicals...) 50
Basic Bibliography
  • M. SPIVAK. Calculus. Cambridge University Press. Fourth edition, 2008
Additional Bibliography
  • B.P. DEMMIDOVICH. Problemas y ejercicios de Anlálisis Matemático. Paraninfo. 1980
  • D. PESTANA, J.M. RODRÍGUEZ, E. ROMERA, E. TOURÍS, V. ÁLVAREZ, A. PORTILLA. Curso práctico de Cálculo y Precálculo. Ariel (Planeta). 2019
  • G.L. BRADLEY, K.J. SMITH. Calculus . Pearson. 2012
  • S.L. SALAS, E. HILLE, G. ETGEN. Calculus one and several variables. Wyley. 10th edition, 2007
  • T.M. APÓSTOL. Mathematical Analysis. Addison-Wesley. 1974

The course syllabus and the academic weekly planning may change due academic events or other reasons.