One Variable Calculus
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The How and Why of One Variable Calculus
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.
Calculus Of One Variable
The Inclusion Of Modern Topics In The Courses Of Studies In Mathematics At The Undergraduate Level Is Very Necessary To Provide A Foundation For Future And Upcoming Topics At The Higher Level. This Book Is Based On This Fact. It Has Been Planned With A View To Provide A Foundation For Future Analysis Courses And To Make Use Of Sister Topics Like Linear And Abstract Algebra In The Forthcoming Years. This Book Contains Six Chapters. Its First Chapter Explains The Basic Concepts On Sets And Numbers Etc.The Second Chapter Deals With The Sequences And Series Of Real Numbers. Third Chapter Discusses The Continuity And Differentiability Of Functions. The Fourth Chapter Deals With Successive Differentiations And Mean Value Theorems. Last Two Chapters Are On Integration And Application Of Calculus. A Unique Feature Of This Book Is That Each Chapter Contains A Large Number Of Illustrations Which Will Help The Students To Understand Through Analytical Approach. The Book Meets Requirements Of B.Sc Part One Courses Of Many Indian Universities Including Those Of Madhya Pradesh.
Practical Analysis in One Variable
Author: Donald Estep
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-04-06
Background I was an eighteen-year-old freshman when I began studying analysis. I had arrived at Columbia University ready to major in physics or perhaps engineering. But my seduction into mathematics began immediately with Lipman Bers’ calculus course, which stood supreme in a year of exciting classes. Then after the course was over, Professor Bers called me into his o?ce and handed me a small blue book called Principles of Mathematical Analysis by W. Rudin. He told me that if I could read this book over the summer,understandmostofit,andproveitbydoingmostoftheproblems, then I might have a career as a mathematician. So began twenty years of struggle to master the ideas in “Little Rudin. ” I began because of a challenge to my ego but this shallow reason was quickly forgotten as I learned about the beauty and the power of analysis that summer. Anyone who recalls taking a “serious” mathematics course for the ?rst time will empathize with my feelings about this new world into which I fell. In school, I restlessly wandered through complex analysis, analyticnumbertheory,andpartialdi?erentialequations,beforeeventually settling in numerical analysis. But underlying all of this indecision was an ever-present and ever-growing appreciation of analysis. An appreciation thatstillsustainsmyintellectevenintheoftencynicalworldofthemodern academic professional. But developing this appreciation did not come easy to me, and the p- sentation in this book is motivated by my struggles to understand the viii Preface most basic concepts of analysis. To paraphrase J.