Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional as a noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that subject. However, the general concept of a functional had previously been introduced in 1887 by the Italian mathematician and physicist Vito Volterra. The theory of nonlinear functionals was continued by students of Hadamard, in particular Fréchet and Lévy. Hadamard also founded the modern school of linear functional analysis further developed by Riesz and the group of Polish mathematicians around Stefan Banach. In modern introductory texts on functional analysis, the subject is seen as the study of vector spaces endowed with a topology, in particular infinite-dimensional spaces. In contrast, linear algebra deals mostly with finite-dimensional spaces, and does not use topology. An important part of functional analysis is the extension of the theory of measure, integration, and probability to infinite dimensional spaces, also known as infinite dimensional analysis. (Wikipedia).
read this to learn functional analysis
read this to learn functional analysis Here is the book on amazon: https://amzn.to/2pMYOql (note this is my affiliate link, I earn a small percentage from qualifying purchases) Do you want to learn functional analysis? In this video I talk about the book that I used to learn this amazing
From playlist Cool Math Stuff
Functional Analysis Book for Beginners
This is a response to a question I received from a viewer. They want to learn functional analysis using the math book Introductory Functional Analysis with Applications by Kreyszig. They also want to know how long to study every day. Do you have any advice for learning functional analysis
From playlist Book Reviews
The Benefits of Functional Architectures | Systems Engineering, Part 3
See the other videos in this series: https://www.youtube.com/playlist?list=PLn8PRpmsu08owzDpgnQr7vo2O-FUQm_fL Functional, logical, and physical architectures are important tools for designing complex systems. We describe what architectures are and how they contribute to the early stages of
From playlist Systems Engineering
What is Functional Programming?
We will discuss the state of functional programming in brief across several languages. Also a discussion on the broader goals of functional programming and this meetup. EVENT: OKC FP 2020 SPEAKER: Scott Murphy PUBLICATION PERMISSIONS: The conference organizer provided Coding Tech wit
From playlist Functional Programming
The Essence of Functional Programming
This talk dives into the origins of functional programming, going all the way back to where the term was first introduced, to see how it evolved over time into our modern understanding of what FP essentially involves. PUBLICATION PERMISSIONS: Original video was published with the Creative
From playlist Functional Programming
Don’t Be Scared Of Functional Programming
As software becomes more and more complex, it is more and more important to structure it well. Well-structured software is easy to write, easy to debug, and provides a collection of modules that can be re-used to reduce future programming costs. Conventional languages place conceptual limi
From playlist Functional Programming
In this video, I talk about the definition of a function and properties of functions. I also go over some examples of how to determine whether a relation is a function or not and how to evaluate functions. Enjoy! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://
From playlist College Algebra
Functional Programming for Beginners: Pure Functions Explained
Why is it that pure functions can’t use mutable states in most cases, and how do you fight mutability by working with immutable values? Check it out in this live coding session by Michal Plachta, the author of Grokking Functional Programming. Watch the full video at: http://mng.bz/J24a 📚
From playlist Functional Programming
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math
Functional Data Analysis Under Shape Constraints - Srivastava - Workshop 2 - CEB T1 2019
Anuj Srivastava (Florida state Univ.) / 13.03.2019 Functional Data Analysis Under Shape Constraints. (Joint work with Sutanoy Dasgupta, Ian Jermyn, and Debdeep Pati). We consider a subarea of functional data analysis, where functions of interest are constrained to have pre-determined sh
From playlist 2019 - T1 - The Mathematics of Imaging
Complex analysis: Introduction
This lecture is part of an online undergraduate course on complex analysis. This is the first lecture, and gives a quick overview of some of the topics that might be covered, such as Cauchy's theorem, analytic continuation, the Riemann zeta function, and the Mandelbrot set. For the oth
From playlist Complex analysis
History of Mathematics - Complex Analysis Part 2: functions of a complex variable. 3rd Yr Lecture
Complex numbers pervade modern mathematics, but have not always been well understood. They first emerged in the sixteenth century from the study of polynomial equations, and were quickly recognised as useful – if slightly weird – mathematical tools. In these lectures (this is the second
From playlist Oxford Mathematics 3rd Year Student Lectures
Object Detection Using Blob Analysis | Student Competition: Computer Vision Training
Learn to detect objects using blob analysis and in doing so, learn how to perform color space conversion, thresholding, morphological operations, and video annotation. Get files: https://bit.ly/2ZBy0q2 Explore the MATLAB and Simulink Robotics Arena: https://bit.ly/2yIgwfS ----------------
From playlist Student Competition: Computer Vision Training
The 3 Best Books on Complex Analysis
I describe my three favorite books for an introduction to complex analysis, and conclude with some remarks about a few other books. Hope this is helpful for both students and instructors! 0:00 Book 1: Greene and Krantz 6:08 Book 2: Stein and Shakarchi 10:14 Book 3: Ablowitz and Fokas 13:4
From playlist Math
Malware Analysis Bootcamp - Introduction To Malware Analysis
Welcome to the Malware Analysis Bootcamp. We will be covering everything you need to know to get started in Malware Analysis professionally. In this video, we will introduce you to malware analysis, the objectives of malware analysis and the various types of malware analysis. Link to slid
From playlist Malware Analysis
In this video, I give a general (and non-technical) overview of the topics covered in an elementary complex analysis course, which includes complex numbers, complex functions, the Cauchy-Riemann equations, Cauchy’s integral formula, residues and poles, and many more! Watch this video if yo
From playlist Complex Analysis
Functional Analysis - Part 2 - Examples for metrics [dark version]
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From playlist Functional Analysis [dark version]