Painless Calculus

by Barron's Educational Series, Christina Pawlowski-Polanish M.S.

Overview

Whether you’re a student or an adult looking to refresh your knowledge, Barron’s Painless Calculus provides review and practice in an easy, step-by-step format.

An essential resource for:

• Virtual Learning
• Homeschool
• Learning pods
• Supplementing classes/in-person learning

Inside you’ll find:

• Examples of all topics, including limits and continuity, derivatives, curve sketching, definite integrals, and much more
• Diagrams, charts, and instructive math illustrations
• Painless tips and common pitfalls
• Math talk boxes that translate complex “math speak” into easy-to-understand language
• Brain Tickler quizzes throughout each chapter to test your progress
   

Product Details

ISBN-13:	9781506273198
Publisher:	Barrons Educational Services
Publication date:	06/01/2021
Series:	Barron's Painless
Edition description:	Third Edition
Pages:	352
Product dimensions:	5.90(w) x 8.90(h) x 0.80(d)
Age Range:	11 - 14 Years

About the Author

About the Author
Christina Pawlowski
Old Bethpage, NY

Christina Pawlowski earned a M.S. in applied Mathematics and a B.A. in Mathematics and Mathematics Education from Hofstra University. She currently teaches high school math, including AP Calculus. Pawlowski is a New York State Master Teacher, a program that celebrates the work of the highest-performing STEM teachers by establishing an expert community dedicated to developing expertise in the areas of content, pedagogy, and students’ families and communities. She has won numerous awards, including the NYS Empire State Excellence in Teaching Award, and was a finalist for the Presidential Award for Excellence in Mathematics and Science Teaching.

About the Publisher
In the 1930s, Manuel H. Barron opened a bookstore in Brooklyn, New York. 

People from the community asked Mr. Barron about books that might be available to help their children study for the New York State Regents exams. After realizing there wasn't anything available, Mr. Barron created his own study guides.

80 years later, Barron's has helped millions of people prepare for their next step.

Table of Contents

How to Use This Book vi

Chapter 1 Limits and Continuity 1

Definition of a Limit 1

Graphic Approach to Limits 2

Graphic Approach to Limits at Infinity 5

Properties of Limits 9

Algebraic Approach to Limits 13

Algebraic Approach to Limits at Infinity 20

Continuity 28

Intermediate Value Theorem 32

Brain Ticklers-The Answers 34

Chapter 2 Differentiation 35

Average Rate of Change 35

Slope of a Tangent Line 38

Definition of a Derivative Function 43

Differentiability 46

Continuity and Differentiability 51

Brain Ticklers-The Answers 52

Chapter 3 Derivatives 53

Notation 53

Properties of Derivatives 55

Power Rule 56

Product Rule 59

Quotient Rule 60

Chain Rule 63

Trigonometric Functions 64

Exponential Functions 66

Logarithmic Functions 68

Sneaky Derivatives 70

Implicit Differentiation 72

Logarithmic Differentiation 76

Inverse Functions 77

Brain Ticklers-The Answers 81

Chapter 4 Applications of Derivatives 83

Equation of a Tangent Line 83

Equation of a Normal Line 86

Local Linear Approximation 88

L'Hopital's Rule 92

Curve Sketching 99

Graphical Representation of the Derivative 118

Second Derivative Test 121

Absolute Maxima and Minima 124

Extreme Value Theorem 126

Optimization 127

Rectilinear Motion 131

Mean Value Theorem 140

Related Rates 142

Brain Ticklers-The Answers 153

Chapter 5 Antidifferentiation 155

Indefinite Integrals 156

Properties of Indefinite Integrals 158

Integral Formulas 160

Integration by U-Substitution 162

Integration by Parts 176

Integration by Partial Fraction Decomposition 185

Integration by Completing the Square 194

Integration with Powers of Trigonometric Functions 197

Integration by Trigonometric Substitutions 201

Brain Ticklers-The Answers 207

Chapter 6 Definite Integrals 209

Notation 209

Properties of Definite Integrals 213

Riemann Sum 218

Trapezoidal Sum 229

Fundamental Theorem of Calculus 237

Mean Value Theorem for Integrals 244

Average Function Value 246

Brain Ticklers-The Answers 250

Chapter 7 Applications of Definite Integrals 251

Area Between Curves 251

Volume of a Solid of Revolution 267

Volume of a Solid with a Known Cross Section 279

Arc Length 289

Rectilinear Motion 292

Brain Ticklers-The Answers 298

Chapter 8 Differential Equations 299

Understanding Differential Equations 299

Separation of Variables 299

Exponential Growth and Decay 304

Logistic Growth 307

Slope Fields 312

Euler's Method 322

Brain Ticklers-The Answers 330

Appendix: Important Derivatives, Formulas, Integrals, Limits, and Theorems 333

Important Derivatives 333

Important Formulas 335

Important Integrals 335

Important Limits 336

Important Theorems 336

Index 339