Identifying Data

2023/24

Subject (*)

Calculus and Numerical Analysis

Code

614G03002

Study programme

Grao en Intelixencia Artificial

Descriptors

Cycle

Period

Year

Type

Credits

Graduate

1st four-month period

First

Basic training

Language

Spanish

Teaching method

Face-to-face

Prerequisites

Department

Matemáticas

Coordinador

Gonzalez Taboada, Maria

E-mail

maria.gonzalez.taboada@udc.es

Lecturers

Cendan Verdes, Jose Jesus

Gonzalez Taboada, Maria

E-mail

jesus.cendan.verdes@udc.es

maria.gonzalez.taboada@udc.es

Web

General description

Nesta materia estudianse técnicas básicas do cálculo diferencial e integral nunha variable, e unha introdución ao cálculo en varias variables. Ademais, presentanse algunhos métodos numéricos básicos para resolver ecuacións non lineais, aproximar funcións dunha variable e as súas derivadas, e resolver sistemas de ecuacións lineais.

Study programme competencies

Code	Study programme competences
A1	Capacidad para utilizar los conceptos y métodos matemáticos y estadísticos para modelizar y resolver problemas de inteligencia artificial.
B2	Que el alumnado sepa aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posea las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio.
B3	Que el alumnado tenga la capacidad de reunir e interpretar datos relevantes (normalmente dentro de su área de estudio) para emitir juicios que incluyan una reflexión sobre temas relevantes de índole social, científica o ética.
B5	Que el alumnado haya desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía.
B7	Capacidad para resolver problemas con iniciativa, toma de decisiones, autonomía y creatividad.
B9	Capacidad para seleccionar y justificar los métodos y técnicas adecuadas para resolver un problema concreto, o para desarrollar y proponer nuevos métodos basados en inteligencia artificial.
C3	Capacidad para crear nuevos modelos y soluciones de forma autónoma y creativa, adaptándose a nuevas situaciones. Iniciativa y espíritu emprendedor.

Learning aims

Learning outcomes	Study programme competences
Know the basics from mathematics that support the remaining subjects of this degree.	A1	B2 B3 B5 B7 B9	C3
Identify, model and solve problems from differential and integral calculus.	A1	B2 B3 B5 B7 B9	C3
Learn the conceptual basis of the mathematical techniques that make up the skeleton of the methods of analysis and modelisation from artificial intelligence.	A1	B2 B3 B5 B7 B9	C3
To handle the concepts of function of several real variables, gradient of a function and approximation of functions, as well as their application to real problems.	A1	B2 B3 B5 B7 B9	C3

Contents

Topic	Sub-topic
Functions of one variable.	Real functions of one real variable. Elementary functions. Limits. Continuity. Bisection method to solve nonlinear equations.
Derivatives	Derivative of a function at one point. Physical and geometrical meaning. Derivability. Calculus of derivatives. Lagrange Mean Value Theorem. Extrema. Concavity and convexity. Newton-Raphson method to solve nonlinear equations. Lagrange interpolation. Numerical differentiation.
Integration	Indefinite integrals: primitives. Riemann's integral. Numerical quadrature. Calculus of areas of plane regions. Calculus of volumes.
Functions of several variables	Functions of several variables. Visualization. Limits and continuity. Differentiability: gradient vector, approximation by the tangent plane, chain rule, directional derivative. Derivatives of higher order. Schwarz's Theorem. Extrema of real functions of several variables.
Numerical solution of linear systems	Condition number of a system of linear equations. Direct and iterative methods.

Planning

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
ICT practicals	A1 B2 B3 B5 B7 B9 C3	20	10	30
Problem solving	A1 B2 B3 B5 B7 B9 C3	10	25	35
Objective test	A1 B2 B3 B5 B7	3	7	10
Guest lecture / keynote speech	A1 B3 B5 B9 C3	30	45	75

Personalized attention		0		0

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies

Methodologies	Description
ICT practicals	In these lectures students will solve problems related with the subject contents using Python.
Problem solving	In these lectures students will solve problems related with the subject contents by hand, with the aim of easing concepts and methods comprehension.
Objective test	To evaluate learning outcomes, there will be a written test on the dates set by the Faculty Board. The test will be oriented essentially to problem solving.
Guest lecture / keynote speech	During these lectures, the teacher will present the subject contents making use of examples to help to the comprehension of the different concepts and methods.

Personalized attention

Methodologies

ICT practicals

Problem solving

Description

During ICT practicals with Python and Problem solving sessions, lecturers will solve students questions about theoretical concepts and their practical applications, reviewing and discussing with each student him/her progress in the assigned practice or problem.

In addition, lecturers will solve the doubts raised by the students in their respective tutorial hours.

With the aim of facilitating following the subject, teachers will make tutorial attention to part-time students and those with an academic dispensation of attendance exemption.

Assessment

Methodologies	Competencies	Description	Qualification
ICT practicals	A1 B2 B3 B5 B7 B9 C3	During ICT practicals lecturers will propose exercises that will qualify up to 50% of the final mark.	50
Objective test	A1 B2 B3 B5 B7	There will be a written exam on the dates set by the Faculty Board. This exam will qualify 50% of the final mark.	50

Assessment comments
In order to pass the subject, it is mandatory to attain at least a qualification of 50%. In the extraordinary call there will be an objective test. It will not be possible to recover the part of the final mark corresponding to continuous assessment. Part-time students and those with academic dispensation of attendance exemption that have not been evaluated of ICT practicals can do a specific exam to recover 50% of the final mark; they can obtain the remaining 50% with the objective test. Fraudulent performance of the tests or evaluation activities, once verified, will directly imply a mark of "0" in the subject in the corresponding call, invalidating any grade obtained in all the evaluation activities for the extraordinary call.

Sources of information

Basic	R.L. Burden, D.J. Faires & A.M. Burden (2017). Análisis Numérico. CENCAGE Learning C. Neuhauser (2004). Matemáticas para ciencias. Pearson R. Johansson (2019). Numerical Python. Apress

Complementary	J.W. Demmel (1997). Applied Numerical Linear Algebra. SIAM G.B Thomas Jr. (2015). Cálculo. Pearson Educación G. Strang & E. Herman (2022). Cálculo (Volumen 1). http://openstax.org/books/cálculo-volumen-1/ G. Strang & E. Herman (2022). Cálculo (Volumen 2). http://openstax.org/books/cálculo-volumen-2/ G. Strang & E. Herman (2022). Cálculo (Volumen 3). http://openstax.org/books/cálculo-volumen-3/ J.E. Marsden & A. Tromba (2018). Cálculo vectorial. Pearson

Recommendations

Subjects that it is recommended to have taken before

Subjects that are recommended to be taken simultaneously

Programming I/614G03006

Algebra/614G03001

Subjects that continue the syllabus

Automata and Formal Languages/614G03017

Fundamentals of Machine Learning/614G03018

Mathematical Optimisation/614G03005

Other comments
Students are recommended to take the subject up to date and consult with the teachers any doubts that may arise.

(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.