The course aims to introduce the mathematical and data analysis methods used in Geosciences and their implementation in Python. The main aim is to achieve an adequate mastery of these methods as well as the ability to develop and use the tools acquired for the study of physical processes involving the Earth system.
Curriculum
teacher profile teaching materials
Complex numbers and trigonometric functions; phasors.
Introduction to signal analysis; definition of a linear time-invariant system; convolution theorem.
Vector calculus; representation in polar, spherical and curvilinear coordinates.
Wave propagation; standing waves.
Fourier series and transform; Nyquist–Shannon sampling theorem.
Introduction to Python programming and exercise on the topics covered in the theory lessons.
Lecture notes by the teacher, covering the topics of the theory lectures.
Python notebooks and datasets used in the exercises.
J. W.-B. Lin, H. Aizenman, E. M. C. Espinel, K. Gunnerson, J. Liu, An Introduction to Python Programming for Scientists and Engineers, Cambridge University Press, 2022, for the Python exercises.
Programme
Matrix calculus and linear systems; matrix factorization (eigenvalues, eigenvectors); rigid rototranslations and associated matrix; least squares method and polynomial regression.Complex numbers and trigonometric functions; phasors.
Introduction to signal analysis; definition of a linear time-invariant system; convolution theorem.
Vector calculus; representation in polar, spherical and curvilinear coordinates.
Wave propagation; standing waves.
Fourier series and transform; Nyquist–Shannon sampling theorem.
Introduction to Python programming and exercise on the topics covered in the theory lessons.
Prerequisiti
Basic knowledge of mathematics (single-variable differential and integral calculus, elementary and trigonometric functions, elements of analytic geometry) and general physics (kinematics, dynamics, oscillations) is required. No prior programming experience is required: the basics of Python are introduced during the course. There are no formal prerequisites.Core Documentation
Lecture notes by the teacher, covering the topics of the theory lectures.
Python notebooks and datasets used in the exercises.
J. W.-B. Lin, H. Aizenman, E. M. C. Espinel, K. Gunnerson, J. Liu, An Introduction to Python Programming for Scientists and Engineers, Cambridge University Press, 2022, for the Python exercises.
Type of delivery of the course
Lessons on the blackboard. Numerical exercises on the topics covered during the course in Python environment.Attendance
Attendance is governed by the degree programme regulations, to which reference is made.Type of evaluation
The exam consists of a written report and an oral exam. Written report Students prepare a report analyzing a geophysical dataset with the methods presented in the course (e.g. least-squares regression, Fourier analysis), implementing the analysis in Python. The report must describe the data, the methods used and the choices made, present the results with figures and discuss them critically, also in relation to the content of the lectures. The data to be analyzed are provided by the teacher; the report is individual; it should be several pages long (fewer than 10); submission of the Python code is recommended; the report must be submitted one week before the first exam session. The report mainly assesses the ability to apply knowledge and understanding, making judgements, communication skills and learning skills. Oral exam The oral exam is an interview in two parts: discussion of the report, in which students present and justify their methodological choices and interpretations, and questions on the theoretical topics of the course. As a rule, two questions are asked on the report and two on theory, over a period of about one hour. The oral exam mainly assesses knowledge and understanding, the ability to apply knowledge and understanding, and communication skills. Evaluation criteria and final grade Assessment takes into account: correctness and completeness of the data analysis; appropriateness and justification of the chosen methods; ability to critically assess results and their limitations; clarity of the report and figures; knowledge and understanding of the theoretical topics; clarity and accuracy of scientific language in the oral presentation. The report and the oral exam contribute 60% and 40% of the final grade respectively; the report must be graded at least sufficient for admission to the oral exam. The final grade is expressed out of 30. teacher profile teaching materials
Complex numbers and trigonometric functions; phasors.
Introduction to signal analysis; definition of a linear time-invariant system; convolution theorem.
Vector calculus; representation in polar, spherical and curvilinear coordinates.
Wave propagation; standing waves.
Fourier series and transform; Nyquist–Shannon sampling theorem.
Introduction to Python programming and exercise on the topics covered in the theory lessons.
Lecture notes by the teacher, covering the topics of the theory lectures.
Python notebooks and datasets used in the exercises.
J. W.-B. Lin, H. Aizenman, E. M. C. Espinel, K. Gunnerson, J. Liu, An Introduction to Python Programming for Scientists and Engineers, Cambridge University Press, 2022, for the Python exercises.
Programme
Matrix calculus and linear systems; matrix factorization (eigenvalues, eigenvectors); rigid rototranslations and associated matrix; least squares method and polynomial regression.Complex numbers and trigonometric functions; phasors.
Introduction to signal analysis; definition of a linear time-invariant system; convolution theorem.
Vector calculus; representation in polar, spherical and curvilinear coordinates.
Wave propagation; standing waves.
Fourier series and transform; Nyquist–Shannon sampling theorem.
Introduction to Python programming and exercise on the topics covered in the theory lessons.
Prerequisiti
Basic knowledge of mathematics (single-variable differential and integral calculus, elementary and trigonometric functions, elements of analytic geometry) and general physics (kinematics, dynamics, oscillations) is required. No prior programming experience is required: the basics of Python are introduced during the course. There are no formal prerequisites.Core Documentation
Lecture notes by the teacher, covering the topics of the theory lectures.
Python notebooks and datasets used in the exercises.
J. W.-B. Lin, H. Aizenman, E. M. C. Espinel, K. Gunnerson, J. Liu, An Introduction to Python Programming for Scientists and Engineers, Cambridge University Press, 2022, for the Python exercises.
Type of delivery of the course
Lessons on the blackboard. Numerical exercises on the topics covered during the course in Python environment.Attendance
Attendance is governed by the degree programme regulations, to which reference is made.Type of evaluation
The exam consists of a written report and an oral exam. Written report Students prepare a report analyzing a geophysical dataset with the methods presented in the course (e.g. least-squares regression, Fourier analysis), implementing the analysis in Python. The report must describe the data, the methods used and the choices made, present the results with figures and discuss them critically, also in relation to the content of the lectures. The data to be analyzed are provided by the teacher; the report is individual; it should be several pages long (fewer than 10); submission of the Python code is recommended; the report must be submitted one week before the first exam session. The report mainly assesses the ability to apply knowledge and understanding, making judgements, communication skills and learning skills. Oral exam The oral exam is an interview in two parts: discussion of the report, in which students present and justify their methodological choices and interpretations, and questions on the theoretical topics of the course. As a rule, two questions are asked on the report and two on theory, over a period of about one hour. The oral exam mainly assesses knowledge and understanding, the ability to apply knowledge and understanding, and communication skills. Evaluation criteria and final grade Assessment takes into account: correctness and completeness of the data analysis; appropriateness and justification of the chosen methods; ability to critically assess results and their limitations; clarity of the report and figures; knowledge and understanding of the theoretical topics; clarity and accuracy of scientific language in the oral presentation. The report and the oral exam contribute 60% and 40% of the final grade respectively; the report must be graded at least sufficient for admission to the oral exam. The final grade is expressed out of 30.