Overview

The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. Contents Prerequisites for calculus Limits and continuity The derivative Applications of the derivative The definite integral Techniques for integration and improper integrals Applications of the definite integral Infinite series, sequences, and approximations

Full Product Details

Author:   Yunzhi Zou ,  Beijing World Publishing Corporation
Publisher:   De Gruyter
Imprint:   De Gruyter
Dimensions:   Width: 17.00cm , Height: 2.30cm , Length: 24.00cm
Weight:   0.797kg
ISBN:  

9783110524628

ISBN 10:   3110524627
Pages:   424
Publication Date:   19 March 2018
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

Chapter 1 Prerequisites for Calculus 1.1 Overview of Calculus 1.2 Sets and Numbers 1.3 Functions 1.4 Exercises Chapter 2 Limits and Continuity 2.1 Rates of Change and Derivatives 2.2 Limits of a Function 2.3 Limits of Sequences 2.4 Squeeze Theorem and Cauchy's Theorem 2.5 Infinitesimal Functions and Asymptotic Functions 2.6 Continuous and Discontinuous Functions 2.7 Some Proofs in Chapter 2 2.8 Exercises Chapter 3 The Derivative 3.1 Derivative of a Function at a Point 3.2 Derivative as a Function 3.3 Derivative Laws 3.4 Derivative of an Inverse Function 3.5 Differentiating a Composite Function - The Chain Rule 3.6 Derivatives of Higher Orders 3.7 Implicit Differentiation 3.8 Functions Defined by Parametric and Polar Equations 3.9 Related Rates of Change 3.10 The Tangent Line Approximation and the Differential 3.11 Derivative Rules-Summar 3.12 Exercises Chapter 4 Applications of the Derivative 4.1 Extreme Values and The Candidate Theorem 4.2 The Mean Value Theorem 4.3 Monotonic Functions and The First Derivative Test 4.4 Extended Mean Value Theorem and the L'opital's Rules 4.5 Taylor's Theorem 4.6 Concave Functions and The Second Derivative Test 4.7 Extreme Values of Functions Revisited 4.8 Curve Sketching 4.9 Solving Equations Numerically 4.10 Curvatures and the Differential of the Arc Length Chapter 5 The Definite Integral 5.1 Definite Integrals and Properties 5.2 The Fundamental Theorem of Calculus 5.3 Numerical lntegration 5.4 Exercises Chapter 6 Techniques for Integration and Improper Integrals 6.1 Indefinite Integrals 6.2 Substitution in Definite Integrals 6.3 Integration by Parts in Definite Integrals 6.4 lmproper Integrals 6.5 Exercises Chapter 7 Applications of the Definite Integral 7.1 Areas Volumes and Arc Lengths 7.2 Applications in Other Disciplines 7.3 Exercises Chapter 8 Infinite Series, Sequences, and Approximations 8.1 Infinite Sequences 8.2 Infinite Series 8.3 Tests for Convergence 8.4 Power Series and Taylor Series 8.5 Fourier Series 8.6 Exercises

Reviews

This is an efficiently compressed entry-level calculus introduction. [...] This is a concisely delivered introduction for engineering students and those on other applied tracks that could support two semesters of study. Tom Schulte in: MAA (18.09.2018), https: //www.maa.org/press/maa-reviews/single-variable-calculus-a-first-step

"""This is an efficiently compressed entry-level calculus introduction. [...] This is a concisely delivered introduction for engineering students and those on other applied tracks that could support two semesters of study."" Tom Schulte in: MAA (18.09.2018), https: //www.maa.org/press/maa-reviews/single-variable-calculus-a-first-step"

This is an efficiently compressed entry-level calculus introduction. [...] This is a concisely delivered introduction for engineering students and those on other applied tracks that could support two semesters of study. Tom Schulte in: MAA (18.09.2018), https: //www.maa.org/press/maa-reviews/single-variable-calculus-a-first-step

This is an efficiently compressed entry-level calculus introduction. [...] This is a concisely delivered introduction for engineering students and those on other applied tracks that could support two semesters of study. Tom Schulte in: MAA (18.09.2018), https: //www.maa.org/press/maa-reviews/single-variable-calculus-a-first-step

Author Information

Yinzhu Zou, Sichuan University, Chengdu, China

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