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Applied Analysis: 20 (Dover Books on Mathematics)

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Book Details:

  • Publisher: Harper Collins India

  • Author: Cornelius Lanczos

  • Language: English

  • Binding: Paperback

  • Edition: New

  • ISBN: 9780486656564

  • Number of Pages: 576

  • Dimensions: 8.5 x 5.5 x 1.3 inches

  • Release Date: 17-03-2003

About The Book:

This essential text by Cornelius Lanczos is designed for graduate and advanced undergraduate students of mathematics, physics, and engineering. The book focuses on mathematical analysis, particularly techniques used for solving engineering and physical problems through the approximation of analytical solutions.

The content is divided into seven chapters, each delving into a specific aspect of mathematical analysis:

  • Chapter I - Algebraic Equations: Discusses methods for finding the roots of algebraic equations, especially in problems related to vibration, flutter, and stability, including techniques like the Bernoulli method.

  • Chapter II - Matrices and Eigenvalue Problems: Provides a systematic development of matrix properties, especially useful in industrial research contexts.

  • Chapter III - Large-Scale Linear Systems: Explores methods like the "spectroscopic method" for solving large matrices and linear systems, as well as perturbation problems.

  • Chapter IV - Harmonic Analysis: Focuses on the Fourier series, particularly its interpolation aspects, useful for representing empirical data.

  • Chapter V - Data Analysis: Discusses techniques for reducing data and determining derivatives of empirical functions, relevant in curve-fitting and tracking problems. It covers two smoothing methods: smoothing in the small and large.

  • Chapter VI - Quadrature Methods: Surveys various quadrature techniques, with an emphasis on Gaussian quadrature and its application in solving boundary value problems.

  • Chapter VII - Power Expansions: Covers the theory of orthogonal function systems, particularly the Chebyshev polynomials.

This comprehensive work remains a classic, invaluable for engineers, physicists, and anyone working in applied mathematics, offering insights into solving complex real-world problems using mathematical analysis.

Ideal for:

  • Graduate and advanced undergraduate students in mathematics, physics, and engineering.

  • Professionals involved in industrial research or anyone working with mathematical methods in the natural sciences.