Lecture

Transforms Properties

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In course

MATH-207(d): Analysis IV

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems. ...

Description

This lecture covers the properties of transforms, including the generalization by recurrence, the vanishing of functions, and the concept of forced trams. It also discusses the proof sketches and the application of these properties in various mathematical contexts.

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Instructors (2)

David Valentin Strütt

Assistanat Vous visitez cette page dans l'optique de rejoindre mon équipe d'asssistant·es pour un de mes cours d'analyse ? Vous trouverez plus d'informations ici. Contributions auteur de polycopiés d'analysecréateur matheminecraftrecord suisse du plus grand nombre de participations à la construction d'un additionneur binaire en dominos (autoproclamé) Je suis né pile le jour de mon anniversaire. Expériences professionnelles Chargé de communication pour MATH et chargé de cours pour la SMA 2019–2024 EPFLCharg

Sébastien Basterrechea

Teaching & PhD Courses Analysis B (for MAN) PREPA-031(b) This course aims at establishing the fundamentals of differential and integral calculus. Analysis I MATH-101(g) We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of one real variable.

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Related concepts (32)

Sine and cosine transforms

In mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency. They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics. The Fourier sine transform of f(t), sometimes denoted by either or , is If t means time, then ξ is frequency in cycles per unit time, but in the abstract, they can be any pair of variables which are dual to each other.

Integral transform

In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the inverse transform. An integral transform is any transform of the following form: The input of this transform is a function , and the output is another function .

Proof theory

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.

GC-content

In molecular biology and genetics, GC-content (or guanine-cytosine content) is the percentage of nitrogenous bases in a DNA or RNA molecule that are either guanine (G) or cytosine (C). This measure indicates the proportion of G and C bases out of an implied four total bases, also including adenine and thymine in DNA and adenine and uracil in RNA. GC-content may be given for a certain fragment of DNA or RNA or for an entire genome.

Applied mathematics

Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

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