Ebook: Approximation Theory: From Taylor Polynomials to Wavelets
- Tags: Approximations and Expansions, Abstract Harmonic Analysis, Fourier Analysis, Functional Analysis, Applications of Mathematics, Signal Image and Speech Processing
- Series: Applied and Numerical Harmonic Analysis
- Year: 2005
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.
Key features and topics:
* Description of wavelets in words rather than mathematical symbols
* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)
* Introduction to infinite series, with emphasis on approximation-theoretic aspects
* Introduction to Fourier analysis
* Numerous classical, illustrative examples and constructions
* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints
* Minimal prerequisites: elementary calculus
* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series
Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.
Key features and topics:
* Description of wavelets in words rather than mathematical symbols
* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)
* Introduction to infinite series, with emphasis on approximation-theoretic aspects
* Introduction to Fourier analysis
* Numerous classical, illustrative examples and constructions
* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints
* Minimal prerequisites: elementary calculus
* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series
Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.
Key features and topics:
* Description of wavelets in words rather than mathematical symbols
* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)
* Introduction to infinite series, with emphasis on approximation-theoretic aspects
* Introduction to Fourier analysis
* Numerous classical, illustrative examples and constructions
* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints
* Minimal prerequisites: elementary calculus
* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series
Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
Content:
Front Matter....Pages i-xi
Approximation with Polynomials....Pages 1-14
Infinite Series....Pages 15-50
Fourier Analysis....Pages 51-82
Wavelets and Applications....Pages 83-104
Wavelets and their Mathematical Properties....Pages 105-136
Back Matter....Pages 137-156
This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.
Key features and topics:
* Description of wavelets in words rather than mathematical symbols
* Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems)
* Introduction to infinite series, with emphasis on approximation-theoretic aspects
* Introduction to Fourier analysis
* Numerous classical, illustrative examples and constructions
* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints
* Minimal prerequisites: elementary calculus
* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series
Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.
Content:
Front Matter....Pages i-xi
Approximation with Polynomials....Pages 1-14
Infinite Series....Pages 15-50
Fourier Analysis....Pages 51-82
Wavelets and Applications....Pages 83-104
Wavelets and their Mathematical Properties....Pages 105-136
Back Matter....Pages 137-156
....