[PDF] The Everything Guide to Calculus I by Greg Hill

The Everything Guide to Calculus Contents

• Prerequisite Skills 
• Start Building with Limits 
• The Importance of Continuity 
• Getting Differentiability Straight 
• Derivatives of Polynomials
• Derivatives of Trigonometric Functions
• The Chain Rule
• Derivatives of Other Functions
• Derivatives of Inverse Trigonometric Functions
• Higher-Order Derivatives
• Graph Analysis Using Derivatives
• Applications of Derivatives 
• The area by Numerical Methods
• The Definite Integral Explored
• The Fundamental Theorem of Calculus
• Methods of Antidifferentiation
• Indefinite Integrals
• The Integral as an Accumulator
• Applications of Integrals

Introduction to The Everything Guide to Calculus PDF

For decades, calculus has struck fear into the hearts of countless high school seniors and first-year college students.

The mere thought of mastering the mysteries of the subject has caused far too many people to give up before they even get started. But for those who gain an understanding of it, calculus is a beautiful integration (no pun intended) of all the math topics that lead up to it.

Calculus uses arithmetic, algebra, geometry, and trigonometry to develop new and fascinating ideas. The most important thing to do as you work through this book is to really believe that you can learn calculus. Its reputation as an unconquerable mountain is totally undeserved.

Centuries ago, the mathematicians Isaac Newton, Gottfried Leibniz, Leonhard Euler, and others worked to develop the ideas of calculus in an attempt to study and understand the world around them. At its most basic, calculus is the mathematics of change.

These mathematicians realized that by thinking in terms of infinitely small increments, they could better understand ideas of limits, rates of change, and even areas and volumes of irregularly shaped regions and objects.

Today, calculus is a vital element in the foundation of many practical fields, such as engineering, biological sciences, medical studies, economics, and even the automobile and film industries.

People in these professions are not necessarily sitting down at their desks and working calculus problems. It is more likely that the tools they use, particularly computer programs, have calculus processes at their core.

Those tools are used to achieve an end or produce a result, and without the help of calculus, the tasks would be significantly more difficult and sometimes even impossible.

This book is intended to remove the mystery of learning calculus. You will see how calculus utilizes many of the foundational ideas introduced in earlier courses of study to develop new ideas.

You will also discover that taken in small steps and developed gradually, the big ideas of calculus are very accessible. It is not the evil monster many people make it out to be.

The book will give the subject relevance by helping you understand how the calculus concept of measuring and exploring summations of infinitely small change shed light on what is happening at any instant, what has happened in the past, and what may happen in the near future.

Currently, global warming is a major concern for environmentalists. Scientists are constantly studying changes in the Earth’s temperature.

Those changes are examined over short intervals to establish current rates of change, and they are studied over longer intervals to get a picture of the long-term impact of the phenomenon. Although it is cloaked here in environmental science, this is the essence of calculus: the study of change. Ironically, calculus itself continues to change in certain respects.

The capabilities of computers and calculators have opened new pathways to understanding the ideas of calculus. Graphing calculators and computer algebra systems reduce some of the challenges that students faced in past decades.

Graphing calculators can rapidly produce graphs, solve equations, and even numerically evaluate derivatives and integrals.

Computer algebra systems can significantly reduce the manipulations necessary for solving complicated equations, taking numerous derivatives, or finding antiderivatives.

Geometry software programs make possible the dynamic visualization of many calculus concepts. Used properly as tools of study, these newer technologies can reduce the mechanical obstacles and sharpen the focus on the big ideas of the course.

The Top 10 Ways to Be Successful in Calculus

1. Develop a solid foundation in algebra, geometry, and trigonometry.
2. Seek a balance between analytic skills and conceptual understanding. Understanding big ideas makes mastering the mechanics much easier.
3. Memorize the facts that are the foundation of the course, including derivative and integral rules and major theorems.
4. Think about most concepts on a microscopic level. Calculus is the study of change on infinitely small intervals and how those changes accumulate.
5. Remember the chain rule. It shows up in almost every derivative and integral.
6. Use visualization tools to make connections between ideas that are important in the subject. Graphing technologies and Internet applets are excellent sources of such tools.
7. Be patient. Master each concept before moving ahead, because the subject builds upon itself incrementally.
8. Read and study from multiple sources. A single explanation of an idea may not make it clear, and there are numerous paths to understand any concept.
9. Find a friend or mentor to discuss the ideas that arise in the course.
10. Look for the beauty and wonder in this subject! Change is everywhere in the world, and calculus helps us analyze and understand it.

The Everything Guide to Calculus I: A Step-by-step Guide to the Basics of Calculus – in Plain English! PDF

Author(s): Greg Hill

Series: Everything series

Publisher: Adams Media, Year: 2011

ISBN: 1440506299

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