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Differential and Integral Calculus: Real Functions of One or Several Real Variables

Differential and Integral Calculus: Real Functions of One or Several Real Variables

          
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About the Book

This book, Differential and Integral Calculus - Real Functions of One or Several Real Variables, presents the fundamental concepts of differential and integral calculus. It is intended for advanced mathematics students as well as professionals requiring a solid command of mathematical analysis tools for technical or scientific tasks.

The book is divided into six major parts:

  1. Differential Calculus:

    • Chapters covering the fundamentals of real functions of one variable, normed vector spaces, and differential operators.
    • Each section is accompanied by solved exercises to reinforce understanding.
  2. Integral Calculus:

    • In-depth discussions on integrals of multivariable functions, line integrals, and surface integrals.
    • Practical exercises to illustrate physical and engineering applications.
  3. Calculus of Variations and Differential Equations:

    • Exploration of the principles of calculus of variations, existence and uniqueness theorems, and dynamical systems.
    • Application of Fourier analysis to evolution equations, with solved exercises to strengthen comprehension.
  4. Analysis on Differential Manifolds:

    • Introduction to differential manifolds, tensor calculus, and Morse theory, with applications in general relativity and geometry.
    • Each chapter is followed by solved exercises, allowing mastery of advanced concepts.
  5. Numerical Methods and Integration Schemes:

    • Presentation of discretization methods, integration schemes, and advanced numerical methods such as finite elements and spectral methods.
    • Practical exercises for solving problems in fluid dynamics and structural mechanics.
  6. Stochastic Calculus and Applications:

    • Introduction to stochastic processes and stochastic differential equations, with applications in finance, biology, and physics.
    • Exercises to apply stochastic calculus to random models and control processes.

Conclusion and Appendices: The book concludes with a chapter dedicated to multivariable integration theorems, including Green's, Stokes', and Gauss' theorems, and their extensions to higher dimensions. The appendices provide a review of fundamental theorems in functional analysis, such as the best approximation theorem, Riesz's lemma, and the Arzelà-Ascoli theorem.

This book is thus a comprehensive and structured guide for anyone seeking to master differential and integral calculus, with particular attention to practical applications in various scientific and technical fields.


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Product Details
  • ISBN-13: 9798336080063
  • Publisher: Amazon Digital Services LLC - Kdp
  • Publisher Imprint: Independently Published
  • Height: 229 mm
  • No of Pages: 120
  • Spine Width: 6 mm
  • Weight: 172 gr
  • ISBN-10: 8336080066
  • Publisher Date: 16 Aug 2024
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Real Functions of One or Several Real Variables
  • Width: 152 mm


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