Calculus For Dummies

Download Calculus For Dummies full books in PDF, epub, and Kindle. Read online Calculus For Dummies ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Calculus For Dummies

Author : Mark Ryan
Publisher : John Wiley & Sons
ISBN 13 : 1119297435
Total Pages : 446 pages
Book Rating : 4.1/5 (192 download)

DOWNLOAD NOW!

Book Synopsis Calculus For Dummies by : Mark Ryan

Download or read book Calculus For Dummies written by Mark Ryan and published by John Wiley & Sons. This book was released on 2016-05-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Slay the calculus monster with this user-friendly guide Calculus 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 concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop 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.

Calculus Workbook For Dummies

Author : Mark Ryan
Publisher : John Wiley & Sons
ISBN 13 : 1119043484
Total Pages : 336 pages
Book Rating : 4.1/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Calculus Workbook For Dummies by : Mark Ryan

Download or read book Calculus Workbook For Dummies written by Mark Ryan and published by John Wiley & Sons. This book was released on 2015-07-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your light-hearted, practical approach to conquering calculus Does the thought of calculus give you a coronary? You aren't alone. Thankfully, this new edition of Calculus Workbook For Dummies makes it infinitely easier. Focusing "beyond the classroom," it contains calculus exercises you can work on that will help to increase your confidence and improve your skills. This hands-on, friendly guide gives you hundreds of practice problems on limits, vectors, continuity, differentiation, integration, curve-sketching, conic sections, natural logarithms, and infinite series. Calculus is a gateway and potential stumbling block for students interested in pursuing a career in math, science, engineering, finance, and technology. Calculus students, along with math students in nearly all disciplines, benefit greatly from opportunities to practice different types of problems—in the classroom and out. Calculus Workbook For Dummies takes you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English, rather than 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. Master differentiation and integration Use the calculus microscope: limits Analyze common functions Score your highest in calculus Complete with tips for problem-solving and traps to avoid, Calculus Workbook For Dummies is your sure-fire weapon for conquering calculus!

Pre-Calculus For Dummies

Author : Yang Kuang
Publisher : John Wiley & Sons
ISBN 13 : 1118168887
Total Pages : 408 pages
Book Rating : 4.1/5 (181 download)

DOWNLOAD NOW!

Book Synopsis Pre-Calculus For Dummies by : Yang Kuang

Download or read book Pre-Calculus For Dummies written by Yang Kuang and published by John Wiley & Sons. This book was released on 2012-06-26 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to the principles of pre-calculus, covering such topics as functions, law of sines and cosines, identities, sequences, series, and binomials.

Pre-Calculus For Dummies

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
ISBN 13 : 1119508711
Total Pages : 545 pages
Book Rating : 4.1/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Pre-Calculus For Dummies by : Mary Jane Sterling

Download or read book Pre-Calculus For Dummies written by Mary Jane Sterling and published by John Wiley & Sons. This book was released on 2018-10-25 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get ahead in pre-calculus Pre-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 manner Includes fresh example problems Practical explanations mirror today’s teaching methods Offers relevant cultural references Whether 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.

Calculus Essentials For Dummies

Author : Mark Ryan
Publisher : John Wiley & Sons
ISBN 13 : 1119591228
Total Pages : 192 pages
Book Rating : 4.1/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Calculus Essentials For Dummies by : Mark Ryan

Download or read book Calculus Essentials For Dummies written by Mark Ryan and published by John Wiley & Sons. This book was released on 2019-04-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts. The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Trigonometry

Author : I.M. Gelfand
Publisher : Springer Science & Business Media
ISBN 13 : 1461201497
Total Pages : 244 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Trigonometry by : I.M. Gelfand

Download or read book Trigonometry written by I.M. Gelfand and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.

Differential Equations For Dummies

Author : Steven Holzner
Publisher : John Wiley & Sons
ISBN 13 : 0470178140
Total Pages : 381 pages
Book Rating : 4.4/5 (71 download)

DOWNLOAD NOW!

Book Synopsis Differential Equations For Dummies by : Steven Holzner

Download or read book Differential Equations For Dummies written by Steven Holzner and published by John Wiley & Sons. This book was released on 2008-06-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

Calculus II For Dummies®

Author : Mark Zegarelli
Publisher : John Wiley & Sons
ISBN 13 : 0470388587
Total Pages : 386 pages
Book Rating : 4.4/5 (73 download)

DOWNLOAD NOW!

Book Synopsis Calculus II For Dummies® by : Mark Zegarelli

Download or read book Calculus II For Dummies® written by Mark Zegarelli and published by John Wiley & Sons. This book was released on 2008-06-02 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. Best of all, it includes practical exercises designed to simplify and enhance understanding of this complex subject.

Quick Calculus

Author : Daniel Kleppner
Publisher : John Wiley & Sons
ISBN 13 : 0471827223
Total Pages : 272 pages
Book Rating : 4.4/5 (718 download)

DOWNLOAD NOW!

Book Synopsis Quick Calculus by : Daniel Kleppner

Download or read book Quick Calculus written by Daniel Kleppner and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quick Calculus 2nd Edition A Self-Teaching Guide Calculus is essential for understanding subjects ranging from physics and chemistry to economics and ecology. Nevertheless, countless students and others who need quantitative skills limit their futures by avoiding this subject like the plague. Maybe that's why the first edition of this self-teaching guide sold over 250,000 copies. Quick Calculus, Second Edition continues to teach the elementary techniques of differential and integral calculus quickly and painlessly. Your "calculus anxiety" will rapidly disappear as you work at your own pace on a series of carefully selected work problems. Each correct answer to a work problem leads to new material, while an incorrect response is followed by additional explanations and reviews. This updated edition incorporates the use of calculators and features more applications and examples. ".makes it possible for a person to delve into the mystery of calculus without being mystified." --Physics Teacher

Calculus For Dummies

Author : Mark Ryan
Publisher : For Dummies
ISBN 13 : 9780764524981
Total Pages : 386 pages
Book Rating : 4.5/5 (249 download)

DOWNLOAD NOW!

Book Synopsis Calculus For Dummies by : Mark Ryan

Download or read book Calculus For Dummies written by Mark Ryan and published by For Dummies. This book was released on 2003-09-09 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein. Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus. Calculus For Dummies is intended for three groups of readers: Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series. Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course. Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more: Real-world examples of calculus The two big ideas of calculus: differentiation and integration Why calculus works Pre-algebra and algebra review Common functions and their graphs Limits and continuity Integration and approximating area Sequences and series Don't buy the misconception. Sure calculus is difficult – but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off – it's simply the next step in a logical progression.

Differential Equations Workbook For Dummies

Author : Steven Holzner
Publisher : John Wiley & Sons
ISBN 13 : 0470543892
Total Pages : 315 pages
Book Rating : 4.4/5 (75 download)

DOWNLOAD NOW!

Book Synopsis Differential Equations Workbook For Dummies by : Steven Holzner

Download or read book Differential Equations Workbook For Dummies written by Steven Holzner and published by John Wiley & Sons. This book was released on 2009-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Get the confidence and the skills you need to master differential equations! Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! More than 100 Problems! Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series THE DUMMIES WORKBOOK WAY Quick, refresher explanations Step-by-step procedures Hands-on practice exercises Ample workspace to work out problems Online Cheat Sheet A dash of humor and fun

Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice)

Author : Patrick Jones
Publisher : John Wiley & Sons
ISBN 13 : 1119883652
Total Pages : 610 pages
Book Rating : 4.1/5 (198 download)

DOWNLOAD NOW!

Book Synopsis Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) by : Patrick Jones

Download or read book Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) written by Patrick Jones and published by John Wiley & Sons. This book was released on 2022-06-01 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practice your way to a higher grade in Calculus! Calculus is a hands-on skill. You’ve gotta use it or lose it. And the best way to get the practice you need to develop your mathematical talents is Calculus: 1001 Practice Problems For Dummies. The perfect companion to Calculus For Dummies—and your class— this book offers readers challenging practice problems with step-by-step and detailed answer explanations and narrative walkthroughs. You’ll get free access to all 1,001 practice problems online so you can create your own study sets for extra-focused learning. Readers will also find: A useful course supplement and resource for students in high school and college taking Calculus I Free, one-year access to all practice problems online, for on-the-go study and practice An excellent preparatory resource for faster-paced college classes Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) is an essential resource for high school and college students looking for more practice and extra help with this challenging math subject. Calculus: 1001 Practice Problems For Dummies (9781119883654) was previously published as 1,001 Calculus Practice Problems For Dummies (9781118496718). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Pre-Calculus Workbook For Dummies

Author : Mary Jane Sterling
Publisher : John Wiley & Sons
ISBN 13 : 1119508800
Total Pages : 375 pages
Book Rating : 4.1/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Pre-Calculus Workbook For Dummies by : Mary Jane Sterling

Download or read book Pre-Calculus Workbook For Dummies written by Mary Jane Sterling and published by John Wiley & Sons. This book was released on 2019-04-02 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Get a handle on pre-calculus in a pinch! If you’re tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you’ll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem. In Pre-Calculus Workbook For Dummies, you’ll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you’ll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations. Get ample review before jumping into a calculus course Supplement your classroom work with easy-to-follow guidance Make complex formulas and concepts more approachable Be prepared to further your mathematics studies Whether you’re enrolled in a pre-calculus class or you’re looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.

Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Author : Patrick Jones
Publisher : John Wiley & Sons
ISBN 13 : 111849671X
Total Pages : 626 pages
Book Rating : 4.1/5 (184 download)

DOWNLOAD NOW!

Book Synopsis Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice) by : Patrick Jones

Download or read book Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice) written by Patrick Jones and published by John Wiley & Sons. This book was released on 2014-08-04 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practice makes perfect—and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus course Helps you refine your understanding of calculus Practice problems with answer explanations that detail every step of every problem The practice problems in 1001 Calculus Practice Problems For Dummies range in areas of difficulty and style, providing you with the practice help you need to score high at exam time.

Business Calculus Demystified

Author : Rhonda Huettenmueller
Publisher : McGraw Hill Professional
ISBN 13 : 0071483438
Total Pages : 457 pages
Book Rating : 4.0/5 (714 download)

DOWNLOAD NOW!

Book Synopsis Business Calculus Demystified by : Rhonda Huettenmueller

Download or read book Business Calculus Demystified written by Rhonda Huettenmueller and published by McGraw Hill Professional. This book was released on 2006-01-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Take the FEAR OUT of Business Calculus Business Calculus Demystified clarifies the concepts and processes of calculus and demonstrates their applications to the workplace. Best-selling math author Rhonda Huettenmueller uses the same combination of winning step-by-step teaching techniques and real-world business and mathematical examples that have succeeded with tens of thousands of college students, regardless of their math experience or affinity for the subject. With Business Calculus Demystified, you learn at your own pace. You get explanations that make differentiation and integration -- the main concepts of calculus -- understandable and interesting. This unique self-teaching guide reinforces learning, builds your confidence and skill, and continuously demonstrates your mastery of topics with a wealth of practice problems and detailed solutions throughout, multiple-choice quizzes at the end of each chapter, and a "final exam" that tests your total understanding of business calculus. Learn business calculus for the real world! This self-teaching course conquers confusion with clarity and ease. Get ready to: Get a solid foundation right from the start with a review of algebra Master one idea per section -- develop complete, comfortable understanding of a topic before proceeding to the next Find a well-explained definition of the derivative and its properties; instantaneous rates of change; the power, product, quotient, and chain rules; and layering different formulas Learn methods for maximizing revenue and profit... minimizing cost... and solving other optimizing problems See how to use calculus to sketch graphs Understand implicit differentiation, rational functions, exponents, and logarithm functions -- learn how to use log properties to simplify differentiation Painlessly learn integration formulas and techniques and applications of the integral Take a "final exam" and grade it yourself! Who says business calculus has to be boring? Business Calculus Demystified is a lively and entertaining way to master this essential math subject!

Calculus Workbook For Dummies

Author : Mark Ryan
Publisher : John Wiley & Sons
ISBN 13 : 047176275X
Total Pages : 306 pages
Book Rating : 4.4/5 (717 download)

DOWNLOAD NOW!

Book Synopsis Calculus Workbook For Dummies by : Mark Ryan

Download or read book Calculus Workbook For Dummies written by Mark Ryan and published by John Wiley & Sons. This book was released on 2005-08-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: From differentiation to integration - solve problems with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or, worse yet, not know where to begin? Have no fear! This hands-on guide focuses on helping you solve the many types of calculus problems you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with limits, continuity, curve-sketching, natural logarithms, derivatives, integrals, infinite series, and more! 100s of Problems! Step-by-step answer sets clearly identify where you went wrong (or right) with a problem The inside scoop on calculus shortcuts and strategies Know where to begin and how to solve the most common problems Use calculus in practical applications with confidence

Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

Author : Mark Ryan
Publisher : John Wiley & Sons
ISBN 13 : 1119909678
Total Pages : 663 pages
Book Rating : 4.1/5 (199 download)

DOWNLOAD NOW!

Book Synopsis Calculus All-in-One For Dummies (+ Chapter Quizzes Online) by : Mark Ryan

Download or read book Calculus All-in-One For Dummies (+ Chapter Quizzes Online) written by Mark Ryan and published by John Wiley & Sons. This book was released on 2023-04-25 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Make calculus more manageable with simplified instruction and tons of practice Calculus All-in-One For Dummies pairs no-nonsense explanations of calculus content with practical examples and practice problems, so you can untangle the difficult concepts and improve your score in any calculus class. Plus, this book comes with access to chapter quizzes online. Dummies makes differentiation, integration, and everything in between more manageable, so you can crush calculus with confidence. Review the foundational basics, then dive into calc lessons that track your class. This book takes you through a full year of high-school calculus or a first semester of college calculus, only explained more clearly. Work through easy-to-understand lessons on everything in a typical calc class Get the score you want and need on standardized tests like AP Calculus Access online chapter quizzes for additional practice Untangle tricky problems and discover clever ways to solve them With clear definitions, concise explanations, and plenty of helpful information on everything from limits and vectors to integration and curve-sketching, Calculus All-in-One For Dummies is the must-have resource for students who want to review for exams or just need extra help understanding the concepts from class.