Ever Learn This?
Laying the Foundation for Calculus 53
5 Take It to the Limit 55
Learn how to gauge a function’s intentions—are they always honorable?
Theory, shmeory How do I do my limit homework? It’s due in an hour!
Ensuring a smooth ride for the rest of the course.
Time to meet the most famous limit of them all face to face Try to do something with your hair!
9 Laying Down the Law for Derivatives 101
All the major rules and laws of derivatives in one delicious smorgasbord!
The chores you’d do day in and day out if your evil stepmother were a mathematician.
How to put a little wiggle in your graph, or why the Puritans were not big fans of calculus.
Introducing position, velocity, acceleration, and Peanut the cat!
The rootin’-tootin’ orneriest hombres of the derivative world
If you can find the area of a rectangle, then you’re in business.
Once you get good at driving forward, it’s time to put it in reverse and see how things go.
16 Applications of the Fundamental Theorem 177
You can do so much with something simple like definite integrals that you’ll feel like a mathematical Martha Stewart.
You’ll have to integrate fractions out the wazoo, so you might as well come to terms with them now.
Advance from integration apprentice to master craftsman.
Who knew that spinning graphs in three dimensions could be so dang fun?
Part 5: Differential Equations, Sequences, Series, and Salutations 219
Just like ordinary equations, but with a creamy filling.
What could be more fun than drawing a ton of teeny-weeny little line segments?
If having an infinitely long list of numbers isn’t exciting enough, try adding them together!
Are you actually going somewhere with that long-winded list of yours?
Series that think they’re functions (I think I saw this on daytime TV.)
How absorbent is your brain? Have you mastered calculus?
Get ready to put yourself to the test.
A Solutions to “You’ve Got Problems” 291
Part 1: The Roots of Calculus 1
What’s the Purpose of Calculus? 4
Finding the Slopes of Curves 4
Calculating the Area of Bizarre Shapes 4
Finding the Average Value of a Function 5
2 Polish Up Your Algebra Skills 13
Walk the Line: Linear Equations 14
Common Forms of Linear Equations 14
You’ve Got the Power: Exponential Rules 17
Breaking Up Is Hard to Do: Factoring Polynomials 19
Method Two: Completing the Square 22
Method Three: The Quadratic Formula 23
3 Equations, Relations, and Functions, Oh My! 25
Graphs to Know by Heart 30
4 Trigonometry: Last Stop Before Calculus 37
The Complete Idiot’s Guide to Calculus, Second Edition viii
What’s Your Sine: The Unit Circle 44
Part 2: Laying the Foundation for Calculus 53
5 Take It to the Limit 55
When Does a Limit Not Exist? 61
What Does Continuity Look Like? 78
The Mathematical Definition of Continuity 79
9 Laying Down the Law for Derivatives 101
Sharp Point in the Graph 102
Finding Equations of Tangent Lines 114
The Complete Idiot’s Guide to Calculus, Second Edition x
The Power Rule for Integration 168
The Fundamental Theorem of Calculus 171
Part One: Areas and Integrals Are Related 171
Part Two: Derivatives and Integrals Are Opposites 172
16 Applications of the Fundamental Theorem 177
Calculating Area Between Two Curves 178
The Mean Value Theorem for Integration 180
Tricky U-Substitution and Long Division 189
Integrating with Inverse Trig Functions 191
Part 5: Differential Equations, Sequences, Series, and Salutations 219
Which Test Do You Use? 252
A Solutions to “You’ve Got Problems” 291
Here’s a new one—a calculus book that doesn’t take itself too seriously! I can honestly say that in all my years as a math major, I’ve never come across a book like this.
Danica McKellar, known for her iconic role as Winnie Cooper on The Wonder Years, is not only an accomplished actress and filmmaker but also a passionate mathematician After taking a four-year detour to major in Mathematics at UCLA, she co-authored a proof for a new math theorem, solidifying her status as a published mathematician Her love for math is evident in her diverse career.
It's important to acknowledge that not everyone is passionate about math, and that's perfectly fine This book isn't aimed at math enthusiasts or dedicated majors seeking exhaustive technical details on every concept Instead, it caters to those who may not have a love for math but are looking for a more accessible understanding of the subject.
This book is designed for biology majors required to complete two semesters of calculus to meet university standards, as well as for any student who has long evaded mathematical formulas but now faces an entire textbook of them It even addresses the plight of students who, like one I knew, changed their major from chemistry to English to escape the demands of calculus.
Mr Kelley offers a comprehensive overview of calculus concepts while equipping you with practical tools and techniques to tackle common challenges faced in calculus courses.
This book offers a refreshing approach to learning calculus, providing friendly and casual explanations that simplify complex concepts without the intimidating jargon found in traditional textbooks Rather than treating it as a conventional textbook, readers can expect a conversational style that engages them, includes humor, and effectively introduces key topics necessary for their calculus course The approachable tone of this book serves as a welcome relief from the often clinical nature of standard math texts.
And oh, Mr Kelley’s colorful metaphors—comparing piecewise functions to Franken- stein’s body parts—well, you’ll understand when you get there.
For a gentle introduction to basic calculus concepts, I recommend reading the chapters of this book first Afterward, revisit your class textbook for fine-tuning; you'll find the explanations clearer and gain confidence in your understanding This approach allows you to better appreciate the specific details required in your class while maintaining control over the level of mathematical precision you wish to achieve.
Congratulations on embarking on the rewarding journey of studying calculus! By choosing to purchase this book as a supplement to your primary textbook, you have made a proactive decision that will enhance your learning experience This book serves as a friendly companion to support you in mastering calculus concepts.
Actress, summa cum laude, Bachelor of Science in Pure Mathematics at UCLA
Many people view learning calculus as an unpleasant experience, often comparing it to a painful encounter with a mule Typically, students take calculus courses out of necessity rather than interest, leading to a perception of the subject as dull and unengaging This lack of enthusiasm is further emphasized by the feeling that calculus offers little reward or enjoyment in return.
Understanding calculus can feel impossible, even if you’ve made efforts like reading the textbook or seeking help from a friend Unfortunately, the complex language of calculus often leaves students feeling frustrated and disconnected, as if they are trying to communicate across a significant cultural barrier.
You may wish for explanations in simpler terms, yet you fear that complex math language will complicate your understanding However, mastering this terminology is essential for passing your course, and you might doubt your abilities The good news is that you have the potential to succeed!
Calculus often appears more daunting than it truly is, and while the subject can be intimidating, teaching it to a large group of high school students in an uncomfortable setting adds to the challenge Having navigated the difficulties of calculus education firsthand, I can share insights that not only inform but also engage and entertain, making the learning experience more approachable and enjoyable.
Join me on an enlightening journey through the world of calculus, where I will serve as your knowledgeable guide With my experience, I aim to equip you with the essential skills needed to navigate this subject confidently Each concept will be explained in clear, accessible language, and I will demonstrate every step of the problem-solving process, ensuring you understand not just the how, but also the why behind each solution Afterward, you will have the opportunity to practice independently, with comprehensive answers provided in the back of the book to support your learning.
Facing challenges can be tough, and not every problem will come easily However, with the right guidance and understanding from someone who empathizes with your struggles, you can overcome any obstacle A little encouragement can make all the difference in your journey to success.
How This Book Is Organized
This book is presented in five parts.
In "The Roots of Calculus," you will discover the significance of calculus and the essential skills it contributes to your mathematical knowledge This section also provides an intriguing glimpse into the history of calculus, which is marked by notable controversies, appealing to both math enthusiasts and those curious about its historical context.
The Complete Idiot’s Guide to Calculus, Second Edition
Before diving into calculus concepts, it's essential to review key algebra and trigonometry skills to ensure a solid foundation.