Course: 2022/2023

Differential Calculus

(18254)

Requirements (Subjects that are assumed to be known)

None

Study of the fundamental Mathematical Analysis of one variable, in particular the Differentiation.

Skills and learning outcomes

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 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

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS]
Knowledge and concepts students must acquire. They will receive the class notes
and will have basic reference texts to facilitate the follow-up of the classes and the development
of subsequent work. Exercises will be solved, they will be practised with
problems by the student and there will be workshops and tests of
assessment to acquire the necessary skills.
TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS]
Individualized attendance (individual tutoring) or in-group (group tutoring)
for students with a teacher.
STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS]
FINAL EXAM. [4 hours with 100% on-site, 0.16 ECTS]
Global assessment of knowledge, skills and capacities acquired throughout the
course.
METHODOLOGIES:
THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual
support in which the subject`s main concepts are developed while providing
material and bibliography to complement student learning.
PRACTICAL CLASS. Resolution of practical cases and problems, posed by the
teacher, and carried out individually or in a group.
TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or
in-group (group tutoring sessions) for students with a teacher as a tutor.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

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 may change due academic events or other reasons.