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About Chris McMullen
Dr. Chris McMullen has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana. Dr. McMullen is also an author of math and science books. Whether in the classroom or as a writer, Dr. McMullen loves sharing knowledge and the art of motivating and engaging students.
Chris McMullen earned his Ph.D. in phenomenological highenergy physics (particle physics) from Oklahoma State University in 2002. Originally from California, Dr. McMullen earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance.
Dr. McMullen is wellknown for:
• engaging students in challenging ideas through creativity
• breaking difficult problems down into manageable steps
• providing clear and convincing explanations to subtle issues
• his mastery of physics and strong background in mathematics
• helping students become more fluent in practical 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 a series of math workbooks on arithmetic, fractions, algebra, geometry, trigonometry, and calculus called the Improve Your Math Fluency Series. Dr. McMullen has also published a variety of science books, including introductions to basic astronomy and chemistry concepts in addition to physics workbooks.
Dr. McMullen is very passionate about teaching. Many students and observers have been impressed with the transformation that occurs when he walks into the classroom, and the interactive engaged discussions that he leads during class time. Dr. McMullen is wellknown for drawing monkeys and using them in his physics examples and problems, using his creativity to inspire students. A stressedout student is likely to be told to throw some bananas at monkeys, smile, and think happy physics thoughts.
Dr. McMullen first published The Visual Guide to Extra Dimensions, Volumes 1 and 2, to share his passion for the geometry and physics of the fourth dimension. Dr. McMullen has coauthored a halfdozen articles on current and future collider searches for large extra dimensions.
In addition to writing and teaching, Dr. McMullen enjoys Scrabble, golf, and chess.
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Blog postWhat is A+ Content? In addition to the product page (and in addition to pages that you can access from Author Central, like the author biography or a From the Author section)…
A Plus Content lets you add additional sections of writing or images to help showcase your book or provide more information about yourself.
It can be a sales tool that you put right on your Amazon product page.
There are several formats to choose from, such as a single wide image (with or withou4 months ago Read more 
Blog postKINDLE VELLA Amazon just launched the new Kindle Vella.
What is Vella? Stories that are told one episode at a time. It has to be new content (not content that has been made available previously), so there shouldn’t be material that you’re familiar with from the past that gets repackaged in Vella. There should only be fresh new content.
There are a few points regarding Vella that appeal to me:
Customers can read the first 3 episodes for free. This is basically equivalent o5 months ago Read more 
Blog postVella is coming soon.
Writers will publish stories in episodes. A single episode may be anywhere from 600 words to 5000 words.
Readers will read stories one episode at a time.
One neat feature that I like is that the author can include optional notes at the end of each episode. An author might share insights into how the story came about or share a personal note. There are many ways that authors can use this space.
Ordinarily, when you read a novel, such notes6 months ago Read more 

Blog postAUSTRALIA KDP Amazon’s Kindle Direct Publishing (KDP) is finally opening a printondemand (POD) facility in Australia, which is great news for authors, small publishers, and Amazon customers in Australia.
The new facility is set to begin its launch on May 19, 2021.
KDP authors should check their paperback pricing options starting on May 12, 2021. On this date, you will be able to check your list price and royalty for Australia, and if necessary, you can adjust the list price7 months ago Read more 
Blog postXL Book Stand My neck was sore from proofreading and revising. Tired of looking down at an angle, I wondered if there was something I could stand atop my desk that could hold books and papers more at eye level. I found this cool book stand on Amazon.
Book Stand I bought the XL size (15.4″ by 11″). I set my 1700 page Webster’s College Dictionary on this, opened to the page I’m using, and it supports it just fine. I also print out my manuscript and set it on the book stand, and it w8 months ago Read more 
Blog postRECENT CHANGES AT KDP There have been several changes to Amazon KDP recently. Have you noticed?
SERIES. One interesting change is the introduction of the series page and the series manager. It seems like this new tool isn’t 100% complete yet, but it’s a giant step in the right direction. From the publishing end, it makes it easier to manage series. Now you get a series landing page and you can even write a series description (by default it uses the description from the first book). <8 months ago Read more 

Blog postSINE, COSINE, AND TANGENT OF 15° AND 75° It is possible to find the sine, cosine, and tangent of 15° and also 75° without using a trig identity (and without using a calculator).
The trick is to begin with a 75°75°30° isosceles triangle, as shown above. Let AB = AC = 2. These are the sides opposite to the 75° angles. The remaining side, BC, is unknown at this point.
With side AB serving as the base, draw an altitude down from point C, as shown8 months ago Read more 
Blog postImage licensed from Shutterstock.
BEWARE OF BOOK PIRATES Earlier this year, after publishing a new book, I visited Amazon to check it out. When I finished inspecting the Amazon detail page for my new book, I clicked the link by my author photo to visit my Author Central page. And, boy, was I surprised by what I found.
(A little background: Author Central now shows only my Kindle eBooks by default. Customers have to click the Paperback tab to find my paperback books.)
I8 months ago Read more 

Blog postEXPANDED DISTRIBUTION Amazon KDP now offers two Expanded Distribution channels. In addition to the usual Expanded Distribution channel for the US, they have added an Expanded Distribution channel for the UK.
Authors and publishers using Amazon’s Kindle Direct Publishing for paperbacks may now add the Expanded Distribution channel for the UK. Each title must be individually enrolled. To sign up for Expanded Distribution in the UK, find a book on your Bookshelf, and go to Page 3 of the9 months ago Read more 
Blog postCHANGES AT AUTHOR CENTRAL If you haven’t already done so, when you next visit Author Central, it will ask you to sign up (even if you are already signed up). This part should be easy. It found my previous information and quickly transferred it over. I checked my biography and author photos, which were the same (although I noticed a couple of duplicate photos and deleted the duplicates). At first, it seemed like my blog feeds were missing, but when I proceeded to add them, I saw that they wer1 year ago Read more

Blog postAMS NOW AVAILABLE IN CANADA AND AUSTRALIA Amazon has made advertising in Canada (print or ebook) and Australia (ebook only) available at AMS via KDP. (Regions previously available include the USA, UK, and continental Europe).
Are you having trouble logging in and setting up an account either in Canada or Australia? If so, this solution may help you:
Don’t go to Reports > Ad Campaigns > Learn more > Canada (or Australia).
Instead, go to your Bookshelf at KDP,1 year ago Read more 

Blog postHere you can find the answer key to Division Facts Practice Book by Chris McMullen, Ph.D. This practice workbook is part of the Improve Your Math Fluency series of workbooks. Most of the workbooks in this series contain the answers at the back of the book. However, the original editions of the basic facts books did not contain the answers. By request, I am adding the answer key for the Division Facts Practice Book to my blog. Here you will find just the answers (not the problems).
Cli1 year ago Read more 
Blog post
ESSENTIAL CALCULUS SKILLS You learn a lot during a calculus course.
How much of this is useful?
Of course, it depends on what you do after calculus.
For example, much of the material is needed in higherlevel math courses.
But how about for physics, engineering, and other applications of calculus?
derivatives of polynomials and trig functions are absolutely essential. You need to practice these until you’re fluent. for integration, sometimes3 years ago Read more 

Blog postCHECKING YOUR ANSWERS: Many math books post the answers to selected questions in the back of the book. Most of my workbooks include the answers to every question in the back of the book.
A few students get a different form of the same answer, and mistakenly believe that the answer in the back of the book is wrong, when it’s really correct.
One common example occurs when the student gets a squareroot in the denominator, like:
The above answer isn’t in standard form. Mo3 years ago Read more 
Blog postCONTENTS This article includes the following sections:
Ways to Challenge Advanced Students How to Make Challenging Algebra Problems A Couple of Sample Problems (from my latest book) 50 Challenging Algebra Problems – Fully Solved (my latest workbook) WAYS TO CHALLENGE ADVANCED STUDENTS Some students catch on quickly, while others struggle to understand.
So how can you engage and challenge the better problemsolvers without blowing the minds of the other students?
If you’re4 years ago Read more 
Blog posthttps://www.amazon.com//dp/1941691250/
ESSENTIAL FRACTION SKILLS Not everyone loves fractions, but fraction skills are important for a number of reasons.
It helps to be fluent with fraction skills when you take algebra, trigonometry, and calculus courses. When you solve for an unknown in algebra, the answer doesn’t always turn out to be a whole number. One reason that cross multiplication is difficult for many students is that the problems inherently involve fractions. In calculus4 years ago Read more 

Blog postPOWERS OF 10 What are powers of 10?
How do you multiply or divide powers of 10?
What are negative powers of 10?
What is 10 raised to the power of zero?
Compare positive and negative powers of 10. Note that the number of zeros is a little different with positive and negative powers of 10. See the chart below.
Examples:
Teachers (and home school educators or parents) are welcome to use the above material regarding powers of 10 for noncommercial4 years ago Read more 
Blog postBlock Sliding Down an Inclined Plane Consider the block sliding down an inclined plane (with friction) illustrated below.
When we apply Newton’s second law to the box, we set the sum of the xcomponents of the forces equal to max and the sum of the ycomponents equal to may.
One of the forces is weight, which equals mg (mass times gravitational acceleration).
The xcomponent of mg has a sine function, whereas the ycomponent of mg has a cosine function:
(mg)x = mg4 years ago Read more 

Blog postSources of Error in Physics This article will help you:
learn how to identify sources of error for a physics experiment describe common mistakes that students make in physics lab reports provide examples of how to describe sources of error What Are Sources of Error? In everyday English, the words “error” and “mistake” may seem similar.
However, in physics, these two words have very different meanings:
An error is something that affects results, which was not plausible to4 years ago Read more 
Blog postUSING ALGEBRA IN ARITHMETIC It’s interesting that algebra can be useful in arithmetic.
Since arithmetic is a prerequsite to learning algebra, most algebra courses don’t focus on how to apply algebra to do arithmetic.
However, you can apply your algebra skills to arithmetic problems.
Following is an example.
Suppose that you would like to multiply 58 times 58, but don’t have a calculator (or cell phone) handy.
One way to do this, which is often taught i5 years ago Read more 
Blog postNUMBER PATTERN PUZZLE Here is an exercise in pattern recognition.
It’s not a linear pattern.
This is an array, so there is a slight geometric element to the pattern.
See if you can figure out the missing numbers in the above puzzle.
Study the four arrays.
See if you can recognize the pattern.
Once you identify the pattern, apply it to the fifth array.
Spoiler alert.
If you scroll down too far…
You will run into the answe6 years ago Read more 

Blog posthttp://amzn.com/1512044288
MATH PUZZLES Here is a math puzzle challenge.
Hint: Each of the 5 patterns below has something in common.
Directions: See if you can figure out which numbers go in the blanks.
1, 2, 4, 6, 10, 12, 16, 18, 22, _, _ 4, 6, 10, 14, 22, 26, 34, 38, _, _ 3, 7, 13, 19, 29, 37, _, _ 4, 9, 25, 49, 121, 169, 289, _, _ 5, 8, 12, 18, 24, 30, 36, 42, 52, 60, 68, _, _ If you need help, you can find hints below.
But don’t scroll too far or yo6 years ago Read more 
 logarithms of various bases and natural logarithms
 the change of base formula
 logarithm rules like the sum and difference formulas
 exponential functions
 hyperbolic functions and their inverses
 graphs of logarithms, exponentials, and hyperbolic functions
 a concise review of exponents in the first chapter
 Euler’s number
 applications such as population growth, continuously compounded interest, and radioactive nuclear decays
 an introduction to complex numbers in the last chapter
 an optional chapter covering the calculus of logarithms, exponentials, and hyperbolic functions
 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
 order of operations; PEMDAS
 fractions, decimals, and percents
 exponents and square roots
 a beginning introduction to working with variables
 ratios and rates
 negative numbers
 other prealgebra skills
 properties of functions
 dealing with radicals
 imaginary numbers
 roots of polynomials
 completing the square
 complex solutions to the quadratic
 synthetic division
 graphing functions
 the fundamental theorem of algebra
 elimination techniques for systems of equations
 equations for parabolas, circles, ellipses, and hyperbolas
 the remainder theorem
 the factor theorem
 conjugate expressions
 inequalities
 and more
 30 fullysolved examples serve as a guide
 70 practice exercises include full solutions
 a quick algebra refresher reviews essential skills
 a chapter on strategies and tips introduces the basic concepts
 age problems
 problems with integers
 relating the digits of a number
 fractions, decimals, and percentages
 average values
 ratios and proportions
 problems with money
 simple interest problems
 rate problems
 two moving objects
 mixture problems
 people working together
 problems with levers
 perimeter and area
 distributing and factoring
 the FOIL method
 cross multiplying
 quadratic equations and the quadratic formula
 how to combine like terms and isolate the unknown
 a variety of rules for working with exponents
 solving systems of equations using substitution, simultaneous equations, or Cramer's rule
 algebra with inequalities
WHAT TO EXPECT: This is a workbook designed to offer plenty of practice with essential skills. It is not a textbook designed to teach trigonometry, but a workbook designed to supplement a student’s instruction in trigonometry. Examples and a brief description of the concepts are included to serve as a quick refresher and a guide. If you need more instruction, you should use this workbook in combination with a textbook. The last chapter involves applications of trig identities, which is a challenging topic that will mostly interest more advanced students. A few chapters are intended to help students memorize the trig functions of common angles like 30, 150, or 315 degrees, which will be especially useful for students who may take exams without a calculator (that’s the case with the MCAT and many math and science courses). There may be more practice than many students need, which is much better than having too little practice. Any extra pages may be helpful for teachers or parents with multiple children.
DESCRIPTION: This Trigonometry Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental trigonometry skills. Every problem can be answered without a calculator, which is very helpful for students who aren’t allowed to use a calculator. This is the case in some trig and physics courses, as well as some standardized exams (like the MCAT).
CONTENTS: This workbook is conveniently divided up into 11 chapters so that students can focus on one trigonometry skill at a time. Skills include the following:
 converting between degrees and radians;
 expressing sine, cosine, tangent, secant, cosecant, and cotangent as fractions by looking at right triangles;
 solving for unknown sides and angles in 45°45°90° and 30°60°90° right triangles;
 determining the sine, cosine, tangent, secant, cosecant, and cotangent of multiples of 30° and 45° up to 360° (working with both degrees and radians);
 practice finding the reference angle for angles in Quadrants II, III, and IV;
 finding the inverse trig functions;
 applying the law of sines and the law of cosines to solve for unknown sides and angles in acute and obtuse triangles;
 solving problems with trig identities (like the angle sum and difference formulas);
 and solving algebraic equations that feature basic trig functions.
EXAMPLES: Each section begins with a few pages of instructions for how to solve the problems followed by some examples. These examples should serve as a useful guide until students are able to solve the problems independently.
ANSWERS: Answers to exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes.
PHOTOCOPIES: The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient if you have multiple children/students or if a child/student needs additional practice.
DESCRIPTION: This combination of physics study guide and workbook focuses on essential problemsolving skills and strategies:
 Fully solved examples with explanations show you stepbystep how to solve standard university physics problems.
 Handy charts tabulate the symbols, what they mean, and their SI units.
 Problemsolving strategies are broken down into steps and illustrated with examples.
 Answers, hints, intermediate answers, and explanations are provided for every practice exercise.
 Terms and concepts which are essential to solving physics problems are defined and explained.
AUTHOR: The author, Dr. Chris McMullen, has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana (and has also taught physics to gifted high school students). Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. He has also published a halfdozen papers on the collider phenomenology of superstringinspired large extra dimensions. Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University (and his M.S. in physics from California State University, Northridge).
Dr. McMullen is wellknown for:
 engaging physics students in challenging ideas through creativity
 breaking difficult problems down into manageable steps
 providing clear and convincing explanations to subtle issues
 his mastery of physics and strong background in mathematics
 helping students become more fluent in practical math skills
SOLUTIONS: The back of the book includes a detailed section of hints, intermediate answers, final answers, and explanations to help you solve each problem one step at a time. It’s like having a physics tutor in the back of the book. (However, if you would prefer complete solutions, search for ISBN 1941691137.)
USES: This study guide workbook can be used to:
 learn how to solve fundamental problems in physics with calculus
 find fullysolved examples of standard physics problems
 develop fluency in physics via practice exercises that include answers, hints, and explanations
 quickly find the most essential physics terms, concepts, and formulas
 prepare for the AP physics exam
 review for standardized exams, such as AP Physics or the fundamentals of the GRE.
 derivatives of polynomials, trig functions, exponentials, and logarithms
 the chain rule, product rule, and quotient rule
 second derivatives (and beyond)
 applications such as related rates, extreme values, and optimization
 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
 nonCartesian coordinate systems
DESCRIPTION: This combination of physics study guide and workbook focuses on essential problemsolving skills and strategies:
 Fully solved examples with explanations show you stepbystep how to solve standard university physics problems.
 Handy charts tabulate the symbols, what they mean, and their SI units.
 Problemsolving strategies are broken down into steps and illustrated with examples.
 Answers, hints, intermediate answers, and explanations are provided for every practice exercise.
 Terms and concepts which are essential to solving physics problems are defined and explained.
AUTHOR: The author, Dr. Chris McMullen, has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana (and has also taught physics to gifted high school students). Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. He has also published a halfdozen papers on the collider phenomenology of superstringinspired large extra dimensions. Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University (and his M.S. in physics from California State University, Northridge).
Dr. McMullen is wellknown for:
 engaging physics students in challenging ideas through creativity
 breaking difficult problems down into manageable steps
 providing clear and convincing explanations to subtle issues
 his mastery of physics and strong background in mathematics
 helping students become more fluent in practical math skills
SOLUTIONS: The back of the book includes a detailed section of hints, intermediate answers, final answers, and explanations to help you solve each problem one step at a time. It's like having a physics tutor in the back of the book. (However, if you would prefer complete solutions, search for ISBN 194169117X.)
USES: This study guide workbook can be used to:
 learn how to solve fundamental problems in physics with calculus
 find fullysolved examples of standard physics problems
 develop fluency in physics via practice exercises that include answers, hints, and explanations
 quickly find the most essential physics terms, concepts, and formulas
 prepare for the AP physics exam
 review for standardized exams, such as AP Physics or the fundamentals of the GRE.
 64 proofs with full solutions.
 9 examples to help serve as a guide.
 A review of terminology, notation, and concepts.
 Similar and congruent triangles
 the Pythagorean theorem
 circles, chords, and tangents
 alternate interior angles
 the triangle inequality
 the angle sum theorem
 quadrilaterals
 regular polygons
 area of plane figures
 inscribed and circumscribed figures
 the centroid of a triangle
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