Marcellini Sbordone - Elementi Di Calcolo is a PDF book that covers the basic topics of calculus, such as limits, derivatives, integrals, sequences and series. The book is written by Paolo Marcellini and Carlo Sbordone, two Italian mathematicians and professors at the University of Florence and the University of Naples Federico II, respectively. The book is intended for students of mathematics, physics, engineering and other sciences that require a solid foundation in calculus.
The book consists of 210 pages and is divided into 10 chapters. The first chapter introduces the concept of real numbers and their properties, such as order, completeness and density. The second chapter deals with functions of one variable and their graphs, limits and continuity. The third chapter studies the derivative of a function and its applications, such as optimization, approximation and curve sketching. The fourth chapter explores the integral of a function and its applications, such as area, volume and work. The fifth chapter extends the concepts of derivatives and integrals to functions of several variables and their partial derivatives, gradients and directional derivatives. The sixth chapter covers differential equations and their methods of solution, such as separation of variables, integrating factors and linear equations. The seventh chapter introduces sequences and series of real numbers and their convergence criteria, such as comparison tests, ratio test and root test. The eighth chapter examines sequences and series of functions and their properties, such as pointwise and uniform convergence, power series and Taylor series. The ninth chapter discusses the concept of vector spaces and their subspaces, linear independence, basis and dimension. The tenth chapter presents some topics of linear algebra, such as matrices, determinants, systems of linear equations and eigenvalues.
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Marcellini Sbordone - Elementi Di Calcolo is a PDF book that can be downloaded for free from various online sources[^1^] [^2^]. It is a useful resource for students who want to learn calculus or review their knowledge. It is also a reference book for teachers who want to prepare lectures or exercises on calculus.
Marcellini Sbordone - Elementi Di Calcolo is not the only calculus book available in PDF format. There are many other books that offer different approaches, levels and topics of calculus for students and teachers. Some of them are:
- Calculus Volume 1 by Gilbert Strang and Edwin �Jed� Herman[^1^]. This book is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Volume 1 covers functions, limits, derivatives, and integration.
- Introduction to Calculus by J.H. Heinbockel[^3^]. This book is a collection of lecture notes for a first-year calculus course. The book covers the basics of calculus, such as limits, continuity, differentiation, integration, applications and transcendental functions.
- Understanding Basic Calculus by S.K. Chung. This book is a self-study guide for students who want to learn calculus or review their knowledge. The book covers the essential topics of a first-year calculus course, such as functions, graphs, limits, derivatives, integrals, exponential and logarithmic functions, trigonometric functions and techniques of integration.
These are just some examples of the many calculus books that can be found online for free. They can be useful resources for anyone who wants to learn more about this fascinating branch of mathematics.
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