Active Calculus 2018
Active Calculus 2018

Author: Matthew Boelkins

Publisher: Createspace Independent Publishing Platform

Published: 2018-08-13

Total Pages: 560

ISBN-13: 9781724458322

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Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Functions of a Real Variable
Functions of a Real Variable

Author: N. Bourbaki

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 343

ISBN-13: 3642593151

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This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

Introduction to Analysis in One Variable
Introduction to Analysis in One Variable

Author: Michael E. Taylor

Publisher: American Mathematical Soc.

Published: 2020-08-11

Total Pages: 247

ISBN-13: 1470456680

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This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

Calculus Volume 3
Calculus Volume 3

Author: Edwin Herman

Publisher:

Published: 2016-03-30

Total Pages: 0

ISBN-13: 9781947172838

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Calculus 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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Introduction to Analysis in Several Variables: Advanced Calculus
Introduction to Analysis in Several Variables: Advanced Calculus

Author: Michael E. Taylor

Publisher: American Mathematical Soc.

Published: 2020-07-27

Total Pages: 445

ISBN-13: 1470456699

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This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.

Calculus
Calculus

Author: Stanley I. Grossman

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 1177

ISBN-13: 148326243X

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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.

Several Real Variables
Several Real Variables

Author: Shmuel Kantorovitz

Publisher: Springer

Published: 2016-02-09

Total Pages: 317

ISBN-13: 3319279564

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This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: •The p-norms on vector space and their equivalence •The Weierstrass and Stone-Weierstrass approximation theorems •The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables •The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem •Applications to Ordinary Differential Equations •Line integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.