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McMullen - Calculus: Essential calculus skills practice workbook with full solutions

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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 lHopitals 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 isnt 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.


**

From the Author

THE IMPROVE YOUR MATH FLUENCY SERIES OF WORKBOOKS
Chris McMullen, Ph.D.


This series of math workbooks is geared toward practicing essential math skills. As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he published this series of math workbooks on arithmetic, fractions, algebra, trigonometry, and more.


CALCULUS-BASED PHYSICS WORKBOOKS





  • Essential Calculus-based Physics Study Guide Workbook

  • 100 Instructive Calculus-based Physics Examples


RELATED BOOKS IN THE IMPROVE YOUR MATH FLUENCY SERIES


50 Challenging Calculus Problems (Fully Solved): Test or review your calculus skills. A variety of problems come in a range of difficulty. How many problems can you solve on your own? ISBN: 1941691269.


Trigonometry Essentials Practice Workbook with Answers. Practice essential skills, including conversion from degrees to radians, trig functions, special triangles, the reference angle, going beyond Quadrant I, inverse trig functions, the law of sines, the law of cosines, and trig identities. Each chapters begins with a short review, including examples. ISBN: 1477497781.


Learn or Review Trigonometry: Essential Skills. This book provides an introduction or review to the basic ideas, concepts, and skills of trigonometry with explanations and examples. ISBN: 194169103X.

Trigonometry Flash Cards
: Memorize the values of trig functions (sine, cosine, and tangent) from 0 to 360 degrees. Available on Kindle. ASIN: B0074EWAUS.


Algebra Essentials Practice Workbook with Answers. Practice essential skills like solving for unknowns, factoring, the quadratic formula, and substitution. Each section begins with a short review, including examples. ISBN: 1453661387.


50 Challenging Algebra Problems (Fully Solved): Test or review your algebra skills. A variety of problems come in a range of difficulty. How many problems can you solve on your own? ISBN: 1941691234.


Systems of Equations: Substitution, Simultaneous, Cramers Rule. Practice solving systems of equations (two equations with two unknowns, or three equations with three unknowns). Includes 2x2 and 3x3 determinants. Each section begins with a short review, including examples. ISBN: 1941691048.


Basic Linear Graphing Skills Practice Workbook. Learn basic coordinate algebra graphing skills, including the four Quadrants, plotting points, finding slope, y-intercept, and the equation for a straight line. Each section begins with a short review, including examples. ISBN: 1941691056.


Type : Math

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Essential Calculus Skills Practice Workbook with Full Solutions Improve Your Math Fluency Chris McMullen, Ph.D. Copyright 2018 Chris McMullen PhD monkeyphysicsblogwordpresscom - photo 1 Copyright 2018 Chris McMullen, Ph.D. monkeyphysicsblog.wordpress.com improveyourmathfluency.com chrismcmullen.com Zishka Publishing All rights reserved. Version 2.07.18A Textbooks > Math > Calculus Study Guides > Workbooks> Math Education > Math > Calculus Paperback ISBN: 978-1-941691-24-3 Contents Introduction This workbook is designed to help practice essential - photo 2 Contents

Introduction
This workbook is designed to help practice essential calculustechniques, especially the art of finding derivatives and performing integrals.Each chapter focuses on one main topic such as how to apply the chain rule orhow to perform an integral with a trigonometric substitution. Every chapter begins with a concise explanation of the mainconcept, followed by a few examples. The examples are fully solved step-by-stepwith explanations, and should serve as a valuable guide for solving thepractice problems.

The solution to every practice exercise is tabulated at theback of the book. A variety of essential calculus skills are covered in thisworkbook. The first chapter starts out simple with derivatives of polynomials,and the difficulty of the lessons progresses as the book continues. Studentswill learn: how to find derivatives and anti-derivatives ofpolynomials how to find derivatives and anti-derivatives oftrigonometric functions how to find derivatives and anti-derivatives of logarithmsand exponentials how to perform definite integrals how to perform multiple integrals a variety of integration techniques May you (or your students) find this workbook usefuland become more fluent with these essential calculus skills.

DERIVATIVES OFPOLYNOMIALS
Given a polynomial term of the form axb(where a is a constant coefficient and b is a constant exponent),to take a derivative with respect to the variable x, first multiply thecoefficient a by the exponent b, and then reduce the exponent by according to the following formula: Note that a few special exponents can make a polynomial looksomewhat different - photo 3 Note that a few special exponents can make a polynomial looksomewhat different: If you see a variable in a denominator, you may bring itto the numerator by negating its exponent according to the following rule: If you see a squareroot rewrite it using an exponent of If no coefficient - photo 4 If you see a squareroot, rewrite it using an exponent of : If no coefficient or exponent is observed the number is implied It may - photo 5 If no coefficient or exponent is observed, the number is implied: It may help to recall the following rules of algebraregarding exponents If - photo 6 It may help to recall the following rules of algebraregarding exponents: If a polynomial includes multiple terms find the derivativeof each term - photo 7 If a polynomial includes multiple terms, find the derivativeof each term individually and then add the results together: For example if y1 4x2 y2 3x and y3 6 this means Note that the - photo 8 For example, if y1 = 4x2, y2= 3x, and y3 = 6, this means: Note that the derivative of a constant equals zero Example Perform the - photo 9 Note that the derivative of a constant equals zero: Example Perform the following derivative with respectto x Example - photo 10Example: Perform the following derivative with respectto x. Example Perform the following derivative with respectto x - photo 12Example Perform the following derivative with respectto x Example - photo 13Example: Perform the following derivative with respectto x. Example Perform the following derivative with respectto u - photo 14Example Perform the following derivative with respectto u Example - photo 15Example: Perform the following derivative with respectto u. Example Perform the following derivative with respectto x - photo 16Example Perform the following derivative with respectto x Example - photo 17Example: Perform the following derivative with respectto x. Example Perform the following derivative with respectto x - photo 18Example Perform the following derivative with respectto x - photo 19Example: Perform the following derivative with respectto x. Chapter 1 Exercises Directions Perform each de - photo 20Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 21Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 22Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 23
Chapter 1 Exercises
Directions: Perform each derivative withrespect to the indicated variable. Chapter 1 Exercises Directions Perform each de - photo 20Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 21Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 22Chapter 1 Exercises Directions Perform each derivative withrespect to the - photo 23
Chapter 1 Exercises
Directions: Perform each derivative withrespect to the indicated variable.

Write your solutions down on a piece of paper. Youcan find the full solution to each problem at the end of this chapter. Part A Part B Chapter 1 Solutions Part A - photo 24 Part B Chapter 1 Solutions Part A - photo 25

Chapter 1 Solutions
Part A Calculus Essential calculus skills practice workbook with full solutions - photo 26
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