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 logarithmsthe chain rule, product rule, and quotient rulesecond derivativeshow to find the extreme values of a functionlimits, including l’Hopital’s ruleantiderivatives of polynomials, trig functions, exponentials, and logarithmsdefinite and indefinite integralstechniques of integration, including substitution, trig sub, and integration by partsmultiple integralsThe goal of this workbook isn’t 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. Read more

PREMIUM PRACTICE FOR A PERFECT 5—WITH THE MOST PRACTICE ONTHE MARKET! Ace the AP Calculus AB Exam with The Princeton Review's comprehensive study guide. Includes 8 full-length Calculus AB practice tests with complete explanations, plus thorough content reviews, targeted test strategies, and access to online extras.Techniques That Actually Work• Tried-and-true strategies to help you avoid traps and beat the test• Tips for pacing yourself and guessing logically• Essential tactics to help you work smarter, not harderEverything You Need for a High Score• Comprehensive content review for all test topics• Up-to-date information on the AP® Calculus AB Exam• Online digital flashcards to review core content• Access to drills, handy study guides, helpful pre-college information, and more via your online Student ToolsPremium Practice for AP Excellence• 8 full-length practice tests (5 in the book, 3 online) withdetailed answer explanations• End-of-chapter drills and targeted practice problem sets• Step-by-step walk-throughs of key calculus formulas and sampl equestions• Digital flashcards online to reinforce your grasp of key AP Calculus AB content Read more

Be prepared for exam day with Barron’s. Trusted content from AP experts!Barron’s AP Calculus Premium, 2025 includes in‑depth content review and practice for the AB and BC exams. It’s the only book you’ll need to be prepared for exam day. Written by Experienced EducatorsLearn from Barron’s‑‑all content is written and reviewed by AP expertsBuild your understanding with comprehensive review tailored to the most recent examsGet a leg up with tips, strategies, and study advice for exam day‑‑it’s like having a trusted tutor by your sideBe Confident on Exam DaySharpen your test‑taking skills with 12 full‑length practice tests‑‑3 AB practice tests and 3 BC practice tests in the book, including one diagnostic test each for AB and BC to target your studying‑‑and 3 more AB practice tests and 3 more BC practice tests online–plus detailed answer explanations for all questionsStrengthen your knowledge with in‑depth review covering all units on the AP Calculus AB and BC examsReinforce your learning with dozens of examples and detailed solutions, plus a series of multiple‑choice practice questions and answer explanations, within each chapterEnhance your problem‑solving skills by working through a chapter filled with multiple‑choice questions on a variety of tested topics and a chapter devoted to free‑response practice exercisesRobust Online PracticeContinue your practice with 3 full‑length AB practice tests and 3 full‑length BC practice tests on Barron’s Online Learning HubSimulate the exam experience with a timed test optionDeepen your understanding with detailed answer explanations and expert adviceGain confidence with scoring to check your learning progress  Read more

PREMIUM PRACTICE FOR A PERFECT 5! Ace the AP Calculus BC Exam with The Princeton Review's comprehensive study guide, which includes 5 full-length practice tests, content reviews, targeted strategies, and access to online extras.Techniques That Actually Work• Tried-and-true strategies to help you avoid traps and beat the test• Tips for pacing yourself and guessing logically• Essential tactics to help you work smarter, not harderEverything You Need for a High Score• Comprehensive content review for all test topics• Up-to-date information on the AP® Calculus BC Exam• Online digital flashcards to review core content• Access to online drills, study plans, a handy list of formulas, helpful pre-college information, and more via your online Student ToolsPremium Practice for AP Excellence• 5 full-length practice tests (3 in the book, 2 online) with detailed answer explanations• End-of-chapter drills and targeted practice problem sets• Step-by-step walk-throughs of key calculus formulas and sample questions• Digital flashcards online to reinforce your grasp of key AP Calculus BC content Read more

From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better.   Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down-to-earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real-world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.  Read more

For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:partial derivativesextreme values with multiple variables (including saddle points)vectors, vector analysis (such as the dot and cross products), and vector calculusthe gradient, divergence, and curlthe main coordinate systems: Cartesian, 2D polar, spherical, and cylindricalpath integrals, surface integrals, and volume integralsflux integrals, center of mass, and moment of inertiatangent and normal vectorsand moreThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors. Read more

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com. Read more

Slay the calculus monster with this user-friendly guideCalculus For Dummies, 2nd Edition makes calculus manageable―even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be.Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is―simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win.Includes foundations in algebra, trigonometry, and pre-calculus conceptsExplores sequences, series, and graphing common functionsInstructs you how to approximate area with integrationFeatures things to remember, things to forget, and things you can't get away withStop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there. Read more

This workbook on ordinary differential equations serves either as a handy supplement to current students or as a useful review for students who have previously studied the material. This book focuses on essential techniques for solving and understanding differential equations. Topics include:first-order differential equationssecond-order differential equationsseparable equationslinear equationshomogeneous equationsexact differential equationsautonomous differential equationsthe Wronskianinitial-value and boundary-value problemsapplications of differential equationspower series solutionsrecurrence relationsLegendre, Chebyshev, Laguerre, and Hermite PolynomialsRodrigues’ formulaand moreThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving differential equations. Read more

From popular math blogger and author of the underground bestseller Math With Bad Drawings, Change Is The Only Constant is an engaging and eloquent exploration of the intersection between calculus and daily life, complete with Orlin's sly humor and wonderfully bad drawings.   Change is the Only Constant is an engaging and eloquent exploration of the intersection between calculus and daily life, complete with Orlin's sly humor and memorably bad drawings. By spinning 28 engaging mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human. Read more

Get ahead in pre-calculusPre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses.Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses.Provides fundamental information in an approachable mannerIncludes fresh example problemsPractical explanations mirror today’s teaching methodsOffers relevant cultural referencesWhether used as a classroom aid or as a refresher in preparation for an introductory calculus course, this book is one you’ll want to have on hand to perform your very best. Read more

CALCULUS: EARLY TRANSCENDENTALS, 9th Edition, provides you with the strongest foundation for a STEM future. James Stewart’s Calculus series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, coauthors Daniel Clegg and Saleem Watson continue his legacy, and their careful refinements retain Stewart’s clarity of exposition and make the 9th Edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide. Read more

This is your integration bible.The climb up Mt Calculus is an arduous one. You limit-gaze at the base of the mountain, cut away at derivatives, but now it’s time to put all your skills to the test.Book of Integrals Is my love letter to calculus and its anti derivatives. These curious little things have so much to unpack and will test your skillset. Come join me and explore certain methods needed to survive these beasts, We will explore from the basics, the most common integrals seen in calculus, and we will uncover some fascinating methods that stump even the best of math nerds. but most importantly, We’ll have some fun.Happy Trails! Read more

Calculus Made Easy by Silvanus P. Thompson and Martin Gardner has long been the most popular calculus primer. This major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader. Read more

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation ­ Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Read more

Master the math needed to excel in data science, machine learning, and statistics. In this book author Thomas Nield guides you through areas like calculus, probability, linear algebra, and statistics and how they apply to techniques like linear regression, logistic regression, and neural networks. Along the way you'll also gain practical insights into the state of data science and how to use those insights to maximize your career. Learn how to: Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon Perform descriptive statistics and hypothesis testing on a dataset to interpret p-values and statistical significance Manipulate vectors and matrices and perform matrix decomposition Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks Navigate practically through a data science career and avoid common pitfalls, assumptions, and biases while tuning your skill set to stand out in the job market Read more

The easy (okay, easier) way to master advanced calculus topics and theoriesCalculus II For Dummies will help you get through your (notoriously difficult) calc class―or pass a standardized test like the MCAT with flying colors. Calculus is required for many majors, but not everyone’s a natural at it. This friendly book breaks down tricky concepts in plain English, in a way that you can understand. Practical examples and detailed walkthroughs help you manage differentiation, integration, and everything in between. You’ll refresh your knowledge of algebra, pre-calc and Calculus I topics, then move on to the more advanced stuff, with plenty of problem-solving tips along the way. Review Algebra, Pre-Calculus, and Calculus I conceptsMake sense of complicated processes and equationsGet clear explanations of how to use trigonometry functionsWalk through practice examples to master Calc IIUse this essential resource as a supplement to your textbook or as refresher before taking a test―it’s packed with all the helpful knowledge you need to succeed in Calculus II. Read more

AP® Calculus AB & BC Crash Course - updated for today's 2025-2026 digital exam!A Higher Score in Less Time!  REA’s Crash Course quick-review study guide is the top choice for AP® students who want to make the most of their study time and earn a high score. Here’s why more AP® teachers and students turn to REA’s AP® Calculus Crash Course: Targeted, Focused Review – Study Only What You Need to Know. REA’s new 3rd edition addresses all the latest 2025-2026 test revisions. We cover only the information tested on the exam, so you can make the most of your valuable study time. Expert Test-taking Strategies and Advice. Authored by a team of AP® Calculus teachers, the book gives you the tips and topics that matter most on exam day. Crash Course relies on the authors’ extensive analysis of the test’s structure and content. By following their advice, you can boost your score in every section of the test. Realistic Practice Questions – a Mini-Test in the Book, a Full-Length Exam Online. Are you ready for your exam? Try our focused practice set inside the book. Then take our full-length online practice exam (one each for Calculus AB & BC) to ensure you're ready for test day. Please note: In the United States, this is a hybrid digital/paper exam. Students complete multiple-choice questions and view free-response questions in the Bluebook app. They handwrite their free-response answers in paper exam booklets that are returned for scoring.  If you're cramming for the exam or looking for a concise course review, Crash Course is the study guide every AP® student needs.About Our AuthorsJoan Marie Rosebush teaches calculus courses at the University of Vermont. Ms. Rosebush has taught mathematics to elementary, middle school, high school, and college students. She taught AP® Calculus via satellite television to high school students scattered throughout Vermont. Ms. Rosebush earned her B.A. degree in elementary education, with a concentration in mathematics, at the University of New York in Cortland, N.Y. She received her Master's Degree in education from Saint Michael's College, Colchester, Vermont.Flavia Banu graduated from Queens College of the City University of New York with a B.A. in Pure Mathematics and an M.A.in Pure Mathematics in 1997. Ms. Banu was an adjunct professor at Queens College where she taught Algebra and Calculus II. Currently, she teaches mathematics at Bayside High School in Bayside, New York, and coaches the math team for the school. Her favorite course to teach is AP Calculus because it requires “the most discipline, rigor and creativity.”About Our Revisions Editor  Stu Schwartz has been teaching mathematics since 1973. For 35 years he taught in the Wissahickon School District, in Ambler, Pennsylvania, specializing in AP Calculus AB and BC and AP Statistics. Mr. Schwartz received his B.S. degree in Mathematics from Temple University, Philadelphia. Mr. Schwartz was a 2002 recipient of the Presidential Award for Excellence in Mathematics Teaching and also won the 2007 Outstanding Educator of the Year Award for the Wissahickon School District. Mr. Schwartz’s resource-rich website, www.mastermathmentor.com, is geared toward helping educators teach AP® Calculus, AP® Statistics, and other math courses. Mr. Schwartz is always looking for ways to provide teachers with new and innovative teaching materials, believing that it should be the goal of every math teacher not only to teach students mathematics, but also to find joy and beauty in math as well. Read more

Paul Lockhart’s Mathematician’s Lament outlined how we introduce math to students in the wrong way. Measurement explains how math should be done. With plain English and pictures, Lockhart makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work. Read more

A comprehensive new illustrated guide to geometry—from New York Times bestselling cartoonist Larry GonickWhat's the point of points? Where do we draw the line? If there are two sides to everything, then what's up with triangles, squares, and polygons?Once again, mathematician-turned-cartoonist Larry Gonick uses his unique gift for witty, lively, and clear exposition to demystify another complex subject: geometry.Moving from the most basic geometrical concepts—planes, lines, and points—through elementary postulates and to elaborate proofs, The Cartoon Guide to Geometry is a comprehensive primer on all the essentials of plane geometry: angles, triangles, area, similarity, and, yes, the Pythagorean theorem. Carefully tailored to the curriculum standards and standardized testing guidelines of the subject, the book provides innovative visuals that develop proofs and constructions with sequential graphics rather than single illustrations. The reader emerges with a deep grasp of key ideas—and has fun getting there. Read more