Academic Year/course:
2023/24
447 - Degree in Physics
26917 - Mathematical Methods for Physics
Syllabus Information
Academic year:
2023/24
Subject:
26917 - Mathematical Methods for Physics
Faculty / School:
100 - Facultad de Ciencias
Degree:
447 - Degree in Physics
ECTS:
6.0
Year:
2
Semester:
Second semester
Subject type:
Compulsory
Module:
---
1. General information
The subject and its expected results respond to the following approaches and objectives:
To know different mathematical resources of the Theory of Complex Variable Functions and the Theory of Probabilities and Statistics that are relevant in the study of physical phenomena
Due to its content, the subject is divided into two blocks: Complex Variable Theory and Probability Theory and Statistics.
Thus, the expected results respond to the following approaches and objectives:
In the part of the Theory of functions of a complex variable, to introduce students to analytical functions, and to prepare them for the use of techniques of complex variable theory that are useful in different branches of Physics.
As for the part of the Theory of Probability and Statistics, the objective is to acquire the fundamental knowledge of this theory for its application to the resolution of problems where probabilistic and statistical aspects are relevant.
The tools acquired will be useful in subjects such as Thermodynamics, Statistical Mechanics and Quantum Mechanics
The approaches and objectives of the subject are aligned with the Sustainable Development Goals (SDGs) of the Agenda 2030 of the United Nations:
2. Learning results
Upon completion of the subject, the student will be competent in the use and understanding of some properties of the analytical functions and their developments in power series. As well as the theory of residues and its application to the calculation of integrals.
Regarding the Probability Theory and Statistics block, the student will be competent in the calculation of probabilities of events, as well as conditional probabilities. They will learn about some of the most common probability distributions . In addition to the understanding of the central limit theorem and its application to physical systems. Regarding the statistics part, the student will know some basic quantities used for the characterization of samples of experimental and numerical data and will be able to obtain point and interval estimators. In addition, they will have the basic knowledge of the use of statistical hypothesis testing.
To pass the subject, the student must demonstrate:
- To be able to carry out derivatives and integrals of complex variable functions.
- The understanding of analytical functions and some of their most important properties.
- Determine Taylor and Laurent developments of analytic functions.
- Use the residue theorem to perform integrals both in the real line and in the complex plane.
- Use counting methods to calculate probabilities.
- Know and apply Bayes' theorem.
- Know the most common probability distributions and some of their properties.
- Obtain some of the most common point and interval estimators and understand some of their properties.
- Use statistical tests to test hypotheses.
3. Syllabus
Block: Complex variable
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Complex variable functions.
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Analytical functions.
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Cauchy-Riemann relations.
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Complex integration.
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Successions and series.
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Taylor and Laurent developments.
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Residues and poles.
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Applications of residue theory.
Block: Probability Theory and Statistics
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Probability interpretations.
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Set theory.
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Axioms of probability.
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Counting methods: permutations and combinations.
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Conditional probabilities.
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Bayes theorem.
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Common probability distributions and their properties.
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Generating functions.
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Central limit theorem.
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Populations and samples.
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Sample parameters.
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Basic point estimators and their properties.
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Confidence intervals.
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Hypothesis testing.
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Goodness-of-fit tests.
4. Academic activities
The subject includes the following activities: lectures, problem sessions and practices.
Dean of the Faculty of Sciences. Computer practice sessions will be developed and agreed upon throughout the semester.
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Problem Sessions: during the teaching period, students will solve various problems on a weekly basis with the teacher's advice
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Exams: approximately 5 hours will be dedicated to solve the theoretical and practical exercises of the exams.
5. Assessment system
The student must demonstrate achievement of the intended learning results through the following assessment activities:
Continuous evaluation of the student's learning through the resolution of problems, questions and other activities proposed by the teacher. The grade for the continuous evaluation will account for 20% of the final grade.
A final exam, which will represent 80% of the grade for students who attend classes in person. The final test consists of two parts: one corresponding to the probability and statistics part and the other to the complex variable part. Each of these two parts represents 50% of the final grade. For a passing final grade, both parts must have a grade greater than or equal to 5.
Passing the subject by means of a single global test:
A final test that will represent 100% of the grade for non-face-to- face students. The final test consists of two parts : one corresponding to the probability and statistics part and the other to the complex variable part. Each of these two parts represents 50% of the final grade. For a passing final grade, both parts must be graded greater or equal to 5.