Calculus Of One Variable

This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis. This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics include the sequences of real numbers, dot product, arc length as a parameter, quadric surfaces, higher-order partial derivatives, and Green's theorem in the plane. This publication is a good source for students learning calculus.

Adopts a user-friendly approach, with an emphasis on worked examples and exercises, rather than abstract theory The computer algebra and graphical package MAPLE is used to illustrate many of the ideas and provides an additional aid to teaching and learning Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web

This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

Richly textured and versatile text characterizes real numbers as a complete, ordered field. Rigorous development of the calculus, plus thorough treatment of basic topics of limits and inequalities. 1968 edition.

First course calculus texts have traditionally been either“engineering/science-oriented” with too little rigor,or have thrown students in the deep end with a rigorous analysistext. The How and Why of One Variable Calculus closes thisgap in providing a rigorous treatment that takes an original andvaluable approach between calculus and analysis. Logicallyorganized and also very clear and user-friendly, it covers 6 maintopics; real numbers, sequences, continuity, differentiation,integration, and series. It is primarily concerned with developingan understanding of the tools of calculus. The author presentsnumerous examples and exercises that illustrate how the techniquesof calculus have universal application. The How and Why of One Variable Calculus presents anexcellent text for a first course in calculus for students in themathematical sciences, statistics and analytics, as well as a textfor a bridge course between single and multi-variable calculus aswell as between single variable calculus and upper level theorycourses for math majors.

The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequences of functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems and examples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Stieltjes and Lebesque integrals are studied together and compared.

Written by three gifted-and funny-teachers, How to Ace Calculus provides humorous and readable explanations of the key topics of calculus without the technical details and fine print that would be found in a more formal text. Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams-all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

The "Classic Text Series" is a collection of books written by the most famous mathematicians of their time and has been proven over the years as the most preferred concept-building tool to learn mathematics. Arihant's imprints of these books are a way of presenting these timeless classics. Compiled by IA MARON, the book "Problems in Calculus of One Variable" has been updated and deals with the modern treatment of complex concepts of Mathematics. Formulated as per the latest syllabus, this complete preparatory guide is accumulated with Problems and Solutions with Answer Keys to enhance problem-solving skills. The unique features accumulated in this book are: 1. Complete coverage of syllabus 2. Chapterwise division of Problems 3. Answers And Hints are provided in a great detailed manner 4. Enhance Mathematical Problem-Solving skills in a lucid manner 5. Works as an elementary textbook to build concepts TABLE OF CONTENT: Introduction to Mathematical Analysis, Differentiation of Functions, Application of Differential Calculus to Investigation of Functions, Indefinite Integrals. Basic Methods of Integration, Basic Classes of Integrable Functions, The Definite Integrals, Applications of the Definite Integral, Improper Integrals, Answers and Hints