Calculus and Mathematical Analysis

This book is an introductory real analysis textbook, presented through the lens of history. That is, it proposes that an effective way to motivate the highly non-intuitve definitions and theorems encountered in an introductory, college level Real Analysis course is via one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context.

This book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the 'big picture' and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis.

This book is a college level text in precalculus and trigonometry.

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry.

I intend this book to be, firstly, an introduction to calculus based on the hyperreal number system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such as Abraham Robinson's Non-standard Analysis or Robert Goldblatt’s Lectures on the Hyperreals.

Gilbert Strang's highly regarded calculus textbook is ideal both as a course companion and for self-study. Examples of the application of calculus to subjects such as physics, engineering and economics are included, as well as many practice questions and illustrative diagrams to assist the reader's grasp of the material.

Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications.

This graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The focus is on beautiful applications of complex analysis to geometry and number theory.

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process.

Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra.

Calculus Made Easy is a popular math book to help modern readers of all levels understand the subject on calculus through simple way and explanation. It's not just theory-based but contains exercises and answers so readers can test and practice the understanding for each chapter.

Not only does it explain the theory (Fractional Calculus) underlying the properties of the generalized operator, but it also illustrates the wide variety of fields to which these ideas may be applied.

Fractional Calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways.

In this book, much emphasis is put on explanations of concepts and solutions to examples. By reading the book carefully, students should be able to understand the concepts introduced and know how to answer questions with justification.

This textbook is an introductory calculus presentation intended for future scientists and engineers. Be sure that you have had the appropriate background material of algebra and trigonometry.