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Functional analysis

Track :

Programming

Lessons no : 32

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What will you learn in this course?
  • Master how to analyze vector spaces using norms, inner products, and topologies for advanced mathematical applications
  • Apply concepts of functional analysis to solve real-world problems in physics, engineering, and data science
  • Identify and utilize key theorems in functional analysis, including Banach and Hilbert space properties
  • Develop skills to evaluate convergence, continuity, and boundedness in infinite-dimensional vector spaces
  • Implement techniques for spectral theory and operator analysis in functional spaces
  • Utilize functional analysis tools to optimize algorithms in machine learning and signal processing
  • Understand the role of dual spaces and linear functionals in mathematical modeling and analysis
  • Apply functional analysis methods to solve differential equations and integral equations effectively
  • Interpret the structure of Banach and Hilbert spaces for research and practical problem-solving
  • Enhance analytical thinking and mathematical rigor in advanced theoretical and applied contexts

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Lessons | 32
Functional Analysis Part 1 Metric Space
00:05:59

Functional Analysis Part 1 Metric Space
Functional Analysis Part 2 Examples for metrics
00:08:15

Functional Analysis Part 2 Examples for metrics
Functional Analysis Part 3 Open and closed sets
00:11:07

Functional Analysis Part 3 Open and closed sets
Functional Analysis Part 4 Sequences limits and closed sets
00:07:13

Functional Analysis Part 4 Sequences limits and closed sets
Functional Analysis Part 5 Cauchy sequences and complete metric spaces
00:07:24

Functional Analysis Part 5 Cauchy sequences and complete metric spaces
Functional Analysis Part 6 Norms and Banach spaces
00:07:57

Functional Analysis Part 6 Norms and Banach spaces
Functional Analysis Part 7 Examples of Banach spaces
00:13:04

Functional Analysis Part 7 Examples of Banach spaces
Functional Analysis Part 8 Inner Products and Hilbert Spaces
00:08:02

Functional Analysis Part 8 Inner Products and Hilbert Spaces
Functional Analysis Part 9 Examples of Inner Products and Hilbert Spaces
00:07:07

Functional Analysis Part 9 Examples of Inner Products and Hilbert Spaces
Functional Analysis Part 10 Cauchy Schwarz Inequality
00:10:06

Functional Analysis Part 10 Cauchy Schwarz Inequality
Functional Analysis Part 11 Orthogonality
00:05:29

Functional Analysis Part 11 Orthogonality
Functional Analysis Part 12 Continuity
00:12:11

Functional Analysis Part 12 Continuity
Functional Analysis Part 13 Bounded Operators
00:10:46

Functional Analysis Part 13 Bounded Operators
Functional Analysis Part 14 Example Operator Norm
00:05:35

Functional Analysis Part 14 Example Operator Norm
Functional Analysis Part 15 Riesz Representation Theorem
00:10:10

Functional Analysis Part 15 Riesz Representation Theorem
Functional Analysis Part 16 Compact Sets
00:10:56

Functional Analysis Part 16 Compact Sets
Functional Analysis Part 17 Arzelà–Ascoli theorem
00:13:30

Functional Analysis Part 17 Arzelà–Ascoli theorem
Functional Analysis Part 18 Compact Operators
00:10:18

Functional Analysis Part 18 Compact Operators
Functional Analysis Part 19 Hölder s Inequality
00:07:42

Functional Analysis Part 19 Hölder s Inequality
Functional Analysis Part 20 Minkowski inequality
00:07:55

Functional Analysis Part 20 Minkowski inequality
Functional Analysis Part 21 Isomorphisms
00:10:39

Functional Analysis Part 21 Isomorphisms
Functional Analysis Part 22 Dual spaces
00:09:17

Functional Analysis Part 22 Dual spaces
Functional Analysis Part 23 Dual space Example
00:13:46

Functional Analysis Part 23 Dual space Example
Functional Analysis Part 24 Uniform Boundedness Principle Banach–Steinhaus Theorem
00:07:05

Functional Analysis Part 24 Uniform Boundedness Principle Banach–Steinhaus Theorem
Functional Analysis Part 25 Hahn–Banach theorem
00:12:10

Functional Analysis Part 25 Hahn–Banach theorem
Functional Analysis Part 26 Open Mapping Theorem
00:05:38

Functional Analysis Part 26 Open Mapping Theorem
Functional Analysis Part 27 Bounded Inverse Theorem and Example
00:06:11

Functional Analysis Part 27 Bounded Inverse Theorem and Example
Spectral Theory 1 Spectrum of Bounded Operators Functional Analysis Part 28
00:07:45

Spectral Theory 1 Spectrum of Bounded Operators Functional Analysis Part 28
Spectral Theory 2 Spectrum of Multiplication Operator Functional Analysis Part 29
00:08:28

Spectral Theory 2 Spectrum of Multiplication Operator Functional Analysis Part 29
Spectral Theory 3 Properties of the spectrum Functional Analysis Part 30
00:10:27

Spectral Theory 3 Properties of the spectrum Functional Analysis Part 30
Spectral Theory 4 Spectral Radius Functional Analysis Part 31
00:11:12

Spectral Theory 4 Spectral Radius Functional Analysis Part 31
Spectral Theory 5 Normal and Self Adjoint Operators Functional Analysis Part 32
00:07:19

Spectral Theory 5 Normal and Self Adjoint Operators Functional Analysis Part 32


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Singepogu mariyababu

Course will help you 2023-05-16

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nice 2022-09-05

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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 .