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Differential and Integral Calculus: Real Functions of One or Several Real Variables
Paperback
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Publisher: Independently Published
Published: Aug 16 2024
Pages: 120
Weight: 0.38
Height: 0.25 Width: 6.00 Depth: 9.00
Language: English
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:
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.
Integral Calculus:
- In-depth discussions on integrals of multivariable functions, line integrals, and surface integrals.
- Practical exercises to illustrate physical and engineering applications.
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.
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.
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.
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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