Calculus for Dummies

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Calculus for Dummies

Format:  Paperback,

364 pages

Publisher: John Wiley & Sons Inc

Publish Date: Sep 2003

ISBN-13: 9780764524981

ISBN-10: 0764524984

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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 calculusThe two big ideas of calculus: differentiation and integrationWhy calculus worksPre-algebra and algebra reviewCommon functions and their graphsLimits and continuityIntegration and approximating areaSequences 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.

Specifications

Publisher: John Wiley & Sons Inc
Publish Date: Sep 2003
ISBN-13: 9780764524981
ISBN-10: 0764524984
Format: Paperback
Number of Pages: 364
Shipping Weight (in pounds): 1.25
Product in Inches (L x W x H): 7.25 x 9.0 x 1.0
Walmart No.: 764524984

Chapter outline

Introductionp. 1
About This Bookp. 1
Conventions Used in This Bookp. 2
How to Use This Bookp. 2
Foolish Assumptionsp. 3
How This Book Is Organizedp. 3
Icons Used in This Bookp. 5
Where to Go from Herep. 6
An Overview of Calculusp. 7
What Is Calculus?p. 9
What Calculus Is Notp. 9
So What Is Calculus Already?p. 10
Real-World Examples of Calculusp. 12
The Two Big Ideas of Calculus: Differentiation and Integrationp. 15
Defining Differentiationp. 15
Investigating Integrationp. 18
Sorting Out Infinite Seriesp. 19
Why Calculus Worksp. 23
The Limit Concept: A Mathematical Microscopep. 23
What Happens When You Zoom Inp. 24
Two Caveats--or Precision, Preschmidgenp. 26
Warming Up with Calculus Prerequisitesp. 29
Pre-Algebra and Algebra Reviewp. 31
Fine-Tuning Your Fractionsp. 31
Absolute Value: Absolutely Easyp. 36
Empowering Your Powersp. 36
Rooting for Rootsp. 37
Logarithms--This Is Not an Event at a Lumberjack Competitionp. 39
Factoring Schmactoring, When Am I Ever Going to Need It?p. 40
Solving Quadratic Equationsp. 42
Funky Functions and Their Groovy Graphsp. 47
What Is a Function?p. 47
What Does a Function Look Like?p. 52
Common Functions and Their Graphsp. 54
Inverse Functionsp. 60
Shifts, Reflections, Stretches, and Shrinksp. 61
The Trig Tangop. 65
Studying Trig at Camp SohCahToap. 65
Two Special Right Trianglesp. 66
Circling the Enemy with the Unit Circlep. 68
Graphing Sine, Cosine, and Tangentp. 74
Inverse Trig Functionsp. 75
Identifying with Trig Identitiesp. 76
Limitsp. 77
Limits and Continuityp. 79
Take It to the Limit--Notp. 79
Linking Limits and Continuityp. 89
The 33333 Limit Mnemonicp. 92
Evaluating Limitsp. 95
Easy Limitsp. 95
The "Real Deal" Limit Problemsp. 97
Evaluating Limits at Infinityp. 106
Differentiationp. 111
Differentiation Orientationp. 113
Differentiating: It's Just Finding the Slopep. 114
The Derivative: It's Just a Ratep. 119
The Derivative of a Curvep. 122
The Difference Quotientp. 124
Average Rate and Instantaneous Ratep. 130
To Be or Not to Be? Three Cases Where the Derivative Does Not Existp. 131
Differentiation Rules--Yeah, Man, It Rulesp. 133
Basic Differentiation Rulesp. 134
Differentiation Rules for Experts--Oh, Yeah, I'm a Calculus Wonkp. 139
Differentiating Implicityp. 146
Getting into the Rhythm with Logarithmic Differentiationp. 148
Differentiating Inverse Functionsp. 149
Scaling the Heights of Higher Order Derivativesp. 150
Differentiation and the Shape of Curvesp. 153
Taking a Calculus Road Tripp. 153
Finding Local Extrema--My Ma, She's Like, Totally Extremep. 157
Finding Absolute Extrema on a Closed Intervalp. 163
Finding Absolute Extrema over a Function's Entire Domainp. 166
Locating Concavity and Inflection Pointsp. 168
Looking at Graphs of Derivatives Till They Derive You Crazyp. 170
The Mean Value Theorem--GRRRRRp. 174
Your Problems Are Solved: Differentiation to the Rescue!p. 177
Getting the Most (or Least) Out of Life: Optimization Problemsp. 177
Yo-Yo a Go-Go: Position, Velocity, and Accelerationp. 181
Related Rates--They Rate, Relativelyp. 189
Tangents and Normals: Joined at the Hipp. 196
Straight Shooting with Linear Approximationsp. 201
Business and Economics Problemsp. 204
Integration and Infinite Seriesp. 209
Intro to Integration and Approximating Areap. 211
Integration: Just Fancy Additionp. 211
Finding the Area under a Curvep. 214
Dealing with Negative Areap. 216
Approximating Areap. 216
Getting Fancy with Summation Notationp. 224
Finding Exact Area with the Definite Integralp. 228
Approximating Area with the Trapezoid Rule and Simpson's Rulep. 231
Integration: It's Backwards Differentiationp. 235
Antidifferentiation--That's Differentiation in Reversep. 235
Vocabulary, Voshmabulary: What Difference Does It Make?p. 237
The Annoying Area Functionp. 237
The Power and the Glory of the Fundamental Theorem of Calculusp. 240
The Fundamental Theorem of Calculus: Take Twop. 244
Finding Antiderivatives: Three Basic Techniquesp. 251
Finding Area with Substitution Problemsp. 258
Integration Techniques for Expertsp. 261
Integration by Parts: Divide and Conquerp. 261
Tricky Trig Integralsp. 268
Your Worst Nightmare: Trigonometric Substitutionp. 274
The As, Bs, and Cxs of Partial Fractionsp. 279
Forget Dr. Phil: Use the Integral to Solve Problemsp. 285
The Mean Value Theorem for Integrals and Average Valuep. 286
The Area between Two Curves--Double the Funp. 289
Finding the Volumes of Weird Solidsp. 292
Analyzing Arc Lengthp. 299
Surfaces of Revolution--Pass the Bottle 'Roundp. 301
L'Hopital's Rule: Calculus for the Sickp. 304
Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!p. 307
Infinite Seriesp. 315
Sequences and Series: What They're All Aboutp. 316
Convergence or Divergence? That Is the Questionp. 321
Alternating Seriesp. 332
Keeping All the Tests Straightp. 336
The Part of Tensp. 339
Ten Things to Rememberp. 341
Your Sunglassesp. 341
a[superscript 2] - b[superscript 2] = (a - b)(a + b)p. 341
0/5 = 0, But 5/0 Is Undefinedp. 341
Anything[superscript 0] = 1p. 342
SohCahToap. 342
Trigonometric Values for 30, 45, and 60 Degree Anglesp. 342
sin[superscript 2 theta] + cos[superscript 2 theta] = 1p. 343
The Product Rulep. 343
The Quotient Rulep. 343
Where You Put Your Keysp. 343
Ten Things to Forgetp. 345
(a + b)[superscript 2] = a[superscript 2] + b[superscript 2]--Wrong!p. 345
[radical]a[superscript 2] + b[superscript 2] = a + b--Wrong!p. 345
Slope = x[subscript 2] - x[subscript 1]/y[subscript 2] - y[subscript 1]--Wrong!p. 345
3a + b/3a + c = b/c--Wrong!p. 346
d/dx[pi superscript 3] = 3[pi superscript 2]--Wrong!p. 346
If k Is a Constant, d/dx kx = k'x + kx'--Wrong!p. 346
The Quotient Rule Is d/dx (u/v) = v'u - vu'/v[superscript 2]--Wrong!p. 346
[function of] x[superscript 2] dx = 1/3x[superscript 3]--Wrong!p. 346
[function of] (sinx) dx = cosx + C--Wrong!p. 347
Green's Theoremp. 347
Ten Things You Can't Get Away Withp. 349
Give Two Answers on Exam Questionsp. 349
Write Illegibly on Examsp. 349
Don't Show Your Work on Examsp. 350
Don't Do All of the Exam Problemsp. 350
Blame Your Study Partner for Your Low Exam Gradep. 350
Tell Your Teacher That You Need an "A" in Calculus to Impress Your Significant Otherp. 350
Complain That Early-Morning Exams Are Unfair Because You're Not a "Morning Personp. 351
Protest the Whole Idea of Gradesp. 351
Pull the Fire Alarm During an Examp. 351
Use This Book as an Excusep. 351
Indexp. 353

Book description

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.

Customer Product Reviews

Rated 4 out of 5★ by 1reviewer.
Rated 4 out of 5★ by Great Book This is a very helpful book for any first year calculus class. There could be more examples, though. Overall, I highly recommend. 05/04/2014
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