Mathématiques
350 documents à télécharger gratuitement
Cours, examens, TD, TP et exercices de mathématiques. Thèmes couverts : algèbre, analyse, probabilités, statistique, optimisation.
This document presents a thesis on the process of skeletonization in imaging, specifically focusing on its application to bone characterization. It discusses various methods and approaches in discrete geometry and image processing. The work aims to enhance techniques for analyzing skeletal structures through automated systems.
Cette thèse présente une méthode de squelettisation appliquée aux images en niveaux de gris, permettant de préserver la topologie tout en s’affranchissant des prétraitements nécessaires à une squelettisation binaire. Une nouvelle approche de paramétrage pour l’amincissement est proposée, appelée Self Contrast Controlled Thinning (SCCT), qui est robuste au bruit et s’adapte au contraste de l’image. La recherche inclut également un protocole d’évaluation de la squelettisation en niveaux de gris, ainsi qu'une structuration du squelette en graphe pour l’analyse morphométrique des objets.
This document covers basic tools used in image processing, outlining essential mathematical transformations applied to improve image quality or extract information. It serves as a foundational resource prior to a practical lab exercise that includes a preliminary assessment of knowledge. Key topics include definitions, arithmetic operations, histograms, convolution, and Fourier transforms.
Ce document aborde la modélisation des empreintes digitales, en mettant l'accent sur les caractéristiques, le traitement informatique et les différentes techniques de modélisation. Il examine également les modèles de classification d'empreintes et présente des propositions de modèles de reconnaissance. À travers une analyse détaillée, les auteurs offrent une contribution significative à la compréhension des empreintes digitales.
This thesis explores the application of the discrete Fourier transform in music theory, analyzing periodicities in sound and their mathematical representations. It covers both the practical use of Fourier analysis in sound analysis and its implications for abstract musical constructs. The work is based on a research internship conducted at IRCAM under the guidance of notable experts in the field.
Ce document traite de la généralisation de la transformée de Fourier pour des signaux non périodiques, permettant de passer du domaine temporel au domaine fréquentiel. Il présente les définitions essentielles, propriétés et exemples de calculs, en mettant en avant l'importance de la transformée de Fourier dans le traitement du signal. Les notions de spectre, énergie spectrale et phase spectrale sont également abordées.
This document presents the fundamental concepts of probability and statistics, focusing on random signals and processes. It covers the notion of probability, theories of probabilities, random variables, and the application of Bayes' theorem. Examples illustrate these concepts, providing a comprehensive overview suitable for students in mathematics or engineering.
This document serves as a comprehensive guide to the definitions and properties of trigonometric functions. It explores the relationships between sine, cosine, and tangent functions, as well as their periodicity and symmetry. Additionally, it includes important formulas and notable values related to trigonometric computations.
This document presents solutions to exercises in the context of quantitative methods, specifically focusing on the development of limit and Taylor series for various mathematical functions. The exercises cover topics such as logarithmic functions and their expansions around specific points. The content is intended for students of a mathematics course in the summer semester of the 2006-2007 academic year.
Ce document contient une série d'exercices sur les développements limités de diverses fonctions. Les exercices varient en complexité, allant des calculs simples aux applications avancées de la théorie des limites. Les étudiants sont encouragés à utiliser les indications et les corrections fournies pour approfondir leur compréhension des concepts mathématiques sous-jacents.
This document contains a series of exercises focused on calculating limited developments of various functions at point zero. It explores the use of Taylor series and asks for order calculations of multiple mathematical functions. The final sections delve into determining limits and equivalents using the established developments.
This document covers limited developments and Taylor series. It provides a detailed explanation of how to approximate functions using polynomials. The content includes formulas, examples, and applications related to Taylor series expansions.
Ce cours vise à enseigner les principales techniques de la statistique descriptive univariée et bivariée, en mettant l'accent sur l'utilisation du langage R pour appliquer ces techniques. Les étudiants apprendront à mettre en œuvre ces méthodes de manière appropriée dans divers contextes. Le cours comprend des heures de théorie et de pratique, ainsi que des références pertinentes.
This document discusses the basics of relational algebra, including unary and binary operators. It explains operations such as selection, projection, union, intersection, difference, and Cartesian product. Each operator is defined with its signature and examples.
This document is a mathematics worksheet focused on teaching students to write whole numbers in numeral and word formats. It includes exercises where numerals are converted into written words and vice versa. The methodology involves providing examples and requiring practical application by the user. The worksheet is part of the 'Infinite Pre-Algebra' series by Kuta Software LLC.
The document contains exercises for reading and writing whole numbers in both numeral and word formats. It includes a series of questions requiring students to convert number phrases into numerals and vice versa. The worksheets are designed for practice in pre-algebra skills.
The document provides guidelines on how to pronounce and write cardinal and ordinal numbers, arithmetic operations, and fractions. It includes examples of reading large numbers, dates, decimals, and percentages, supplemented by arithmetic practice and word-based numerical expressions. Additionally, it highlights tasks to reinforce numerical literacy, encouraging users to explore number formats in various contexts. It serves as an introductory text for understanding and practicing numerical interpretation.
This document covers the concepts of limits in calculus, focusing on the comparison and equivalence of functions, successive derivatives, and the Taylor series. It includes theorems related to the differentiability of functions at a point and presents formulas for approximating functions using polynomials. Applications of these theorems are illustrated, particularly in the context of exponential and trigonometric functions.
This document serves as a concise aide mémoire for understanding probability theory, covering fundamental concepts like probability spaces, counting principles, and conditional probabilities. It provides insights into discrete and continuous random variables, as well as various models of probability. The guide is essential for students and practitioners in the field of mathematics and statistics.
This document defines a fraction F as the ratio of two integers p and q, where p is the dividend and q is the divisor, with q requiring to be non-zero. It explains two primary operations on fractions: addition, which combines fractions using a common denominator, and multiplication, which multiplies both numerators and denominators. The notes include examples and mathematical formulations for these operations and pose a question to define a software-based class for fraction manipulation.
This document discusses the approximation of functions using polynomials, focusing on polynomial interpolation, stability, and convergence. It also covers the application of Newton-Cotes quadrature for numerical integration and the methods of Taylor series for local approximation. Key concepts include Lagrange interpolation, Chebyshev points, and uniform approximation.
This document serves as a study guide for the STT-1000 exam on probabilities and statistics. It outlines key concepts, including probability distributions, the central limit theorem, and descriptive statistics for sample observations. Students are provided with essential formulas and descriptions for various statistical functions.
Ce document contient une série d'exercices portant sur la statistique descriptive. Les exercices incluent des calculs de sommes, des spécifications de populations statistiques, et des analyses de données collectées. Des questions sur la représentation graphique et l'interprétation des résultats sont également proposées.
This document contains a series of statistical exercises focused on descriptive statistics, covering topics such as frequency distribution, median calculations, quartiles, and variance. The exercises involve practical applications, including analysis of family expenditures, temperatures across cities, employee salaries, and unpaid invoices. It aims to assess understanding and application of statistical principles.