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Numerical Methods

Code: 107594
Credits: 6
2026/2027
Degree programme Type Course
Physics FB 2

Contact lecturer

Name :
Carles Navau Ros
Email :
carles.navau@uab.cat

Teaching staff

José María Escartin Esteban

Group languages

You can consult this information at the end of the document.

Prerequisites

It is important to have successfully completed the course in Experimental Physics, Data Processing, and Programming.

Objectives

Upon successful completion of this course, students will be able to:

  1. Understand the fundamental principles of the numerical methods most commonly used in physics, as well as their range of applications, limitations, and sources of error.
  2. Implement numerical algorithms to solve scientific problems using appropriate programming languages and computational tools.
  3. Apply numerical methods to physics problems involving linear algebra, equation solving, numerical integration, numerical differentiation, and the solution of differential equations.
  4. Critically analyze the results obtained through numerical computation by assessing their accuracy, stability, and computational efficiency, and by comparing them with analytical solutions whenever possible.


Learning outcomes

  • CM01 (Solve problems in the sciences using the fundamentals of the main areas of physics in a professional context.) Solve problems in the sciences using the fundamentals of the main areas of physics in a professional context.
  • CM02 (Evaluate the principal magnitudes involved in a given basic physical system, manipulating them according to fundamental physical laws to draw conclusions about the predictable behaviour of the system under study.) Evaluate the principal magnitudes involved in a given basic physical system, manipulating them according to fundamental physical laws to draw conclusions about the predictable behaviour of the system under study.
  • KM01 (State Newton's laws and their relationship with the movement of particles and fluids.) State Newton's laws and their relationship with the movement of particles and fluids.
  • SM01 (Correctly use scientific language, magnitudes and units associated with fundamental physical concepts.) Correctly use scientific language, magnitudes and units associated with fundamental physical concepts.
  • SM02 (Apply the theory, fundamentals and numerical methods of general physics to the resolution of simple problems and the explanation of experimental phenomena.) Apply the theory, fundamentals and numerical methods of general physics to the resolution of simple problems and the explanation of experimental phenomena.

Contents

1. Basic concepts.


Numerical error.

Discretization.

Normalization.


2. Solution of nonlinear equations.


Newton-Raphson method.

Systems of nonlinear equations.


3. Numerical differentiation.


4. Numerical integration.


5. Solution of differential equations.


Euler's method.

Runge-Kutta methods.

Other methods (shooting, ...).


6. Solution of partial differential equations.


Finite elements and finite differences.

Implicit and explicit schemes.

Systems of linear equations.


7. Modeling of complex systems.


Concepts of modeling and simulation.

Simulation of physical systems. Examples.

Learning activities and methodology

Title Hours ECTS Learning outcomes
Theory lessons 21 0.84 CM01, CM02, KM01, SM01, SM02
Simulation 28 1.12 CM01, CM02, KM01, SM01, SM02
Autonomous work 95 3.8 CM01, CM02, KM01, SM01, SM02

Theory classes. Main topics explained by the lecturer.

Practice classes. The students practice the method learned through simulations of physical systems.


Details to be determined

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Exams TBD 6 0.24 CM01, CM02, KM01, SM01, SM02
Simulation Work TBD 0 0 CM01, CM02, KM01, SM01, SM02

To be determined

Bibliography

1. Introducción al Análisis Numérico. A. Ralston, Limusa-Wiley.

2. Análisis numérico. Las matemáticas del cálculo científico, D. Kinkaid, D. Cheney, Wesley Iberoamericana.

3. Mètodes numèrics per a la física, R. Guardiola, E. Higón, J. Ros, Materials 9, Universitat de València.

4. Métodos numéricos para la Física i la Ingeniería. Luis Vázquez, Salvador Jiménez, CarlosAguirre, Pedro José Pascual, McGraw Hill.


Software

The installation and use of the needed software will be explained.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan second semester morning-mixed
(PLAB) Practical laboratories 1 Catalan second semester morning-mixed
(PLAB) Practical laboratories 2 Catalan second semester morning-mixed
(PLAB) Practical laboratories 3 Catalan second semester morning-mixed
(PLAB) Practical laboratories 4 Catalan second semester morning-mixed