Essential Calculus Skills Practice Workbook with Full Solutions

Book Description

The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook (with full solutions to every problem) to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:

• derivatives of polynomials, trig functions, exponentials, and logarithms
• the chain rule, product rule, and quotient rule
• second derivatives
• how to find the extreme values of a function
• limits, including l’Hopital’s rule
• antiderivatives of polynomials, trig functions, exponentials, and logarithms
• definite and indefinite integrals
• techniques of integration, including substitution, trig sub, and integration by parts
• multiple integrals

The goal of this workbook isn’t to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering.

Table of Contents

Chapter 1 Derivatives Of Polynomials
Chapter 2 The Chain Rule, Product Rule, And Quotient Rule
Chapter 3 Derivatives Of Trig Functions
Chapter 4 Derivatives Of Exponentials
Chapter 5 Derivatives Of Logarithms
Chapter 6 Second Derivatives
Chapter 7 Extreme Values
Chapter 8 Limits And L’Hôpital’S Rule
Chapter 9 Integrals Of Polynomials
Chapter 10 Definite Integrals
Chapter 11 Integrals Of Trig Functions
Chapter 12 Integrals Of Exponentials And Logarithms
Chapter 13 Integration By Polynomial Substitution
Chapter 14 Integration By Trigonometric Substitution
Chapter 15 Integration By Parts
Chapter 16 Multiple Integrals

中文：

书名：Essential Calculus Skills Practice Workbook with Full Solutions

作者克里斯·麦克马伦(Chris McMullen)博士拥有20多年向物理专业学生教授数学技能的经验。他准备了这本全面的练习册(每个问题都有完整的解决方案)来分享他掌握微积分的策略。本工作簿涵盖了各种 微积分基本技能, including:

• 多项式、三角函数、指数和对数的导数
• 链式规则、乘积规则和商规则
• 二阶导数
• how to find the extreme values of a function
• 极限，包括l‘Hopital规则
• 多项式、三角函数、指数和对数的反导数
• 定积分和不定积分
• 集成技术，包括替换、触发子和分部集成
• 重积分

这本练习册的目标不是涵盖微积分的每一个可能的主题，而是专注于将微积分应用于其他学科所需的最基本的技能，如物理或工程。

Table of Contents

Chapter 1 Derivatives Of Polynomials
第二章链式规则、乘积规则和商规则
第三章Trig函数的导数
第四章指数导数
第5章对数的导数
第六章二阶导数
第七章极值
第八章极限与洛佩特法则
第九章多项式的积分
第十章定积分
第11章TRIG函数的积分
第12章指数和对数的积分
第十三章多项式代换积分
第十四章三角代换积分
第十五章分块集成
Chapter 16 Multiple Integrals