Calculus for Dummies Book

	Introduction	1
	About This Book	1
	Conventions Used in This Book	2
	How to Use This Book	2
	Foolish Assumptions	3
	How This Book Is Organized	3
	Icons Used in This Book	5
	Where to Go from Here	6
Part I	An Overview of Calculus	7
Chapter 1	What Is Calculus?	9
	What Calculus Is Not	9
	So What Is Calculus Already?	10
	Real-World Examples of Calculus	12
Chapter 2	The Two Big Ideas of Calculus: Differentiation and Integration	15
	Defining Differentiation	15
	Investigating Integration	18
	Sorting Out Infinite Series	19
Chapter 3	Why Calculus Works	23
	The Limit Concept: A Mathematical Microscope	23
	What Happens When You Zoom In	24
	Two Caveats--or Precision, Preschmidgen	26
Part II	Warming Up with Calculus Prerequisites	29
Chapter 4	Pre-Algebra and Algebra Review	31
	Fine-Tuning Your Fractions	31
	Absolute Value: Absolutely Easy	36
	Empowering Your Powers	36
	Rooting for Roots	37
	Logarithms--This Is Not an Event at a Lumberjack Competition	39
	Factoring Schmactoring, When Am I Ever Going to Need It?	40
	Solving Quadratic Equations	42
Chapter 5	Funky Functions and Their Groovy Graphs	47
	What Is a Function?	47
	What Does a Function Look Like?	52
	Common Functions and Their Graphs	54
	Inverse Functions	60
	Shifts, Reflections, Stretches, and Shrinks	61
Chapter 6	The Trig Tango	65
	Studying Trig at Camp SohCahToa	65
	Two Special Right Triangles	66
	Circling the Enemy with the Unit Circle	68
	Graphing Sine, Cosine, and Tangent	74
	Inverse Trig Functions	75
	Identifying with Trig Identities	76
Part III	Limits	77
Chapter 7	Limits and Continuity	79
	Take It to the Limit--Not	79
	Linking Limits and Continuity	89
	The 33333 Limit Mnemonic	92
Chapter 8	Evaluating Limits	95
	Easy Limits	95
	The "Real Deal" Limit Problems	97
	Evaluating Limits at Infinity	106
Part IV	Differentiation	111
Chapter 9	Differentiation Orientation	113
	Differentiating: It's Just Finding the Slope	114
	The Derivative: It's Just a Rate	119
	The Derivative of a Curve	122
	The Difference Quotient	124
	Average Rate and Instantaneous Rate	130
	To Be or Not to Be? Three Cases Where the Derivative Does Not Exist	131
Chapter 10	Differentiation Rules--Yeah, Man, It Rules	133
	Basic Differentiation Rules	134
	Differentiation Rules for Experts--Oh, Yeah, I'm a Calculus Wonk	139
	Differentiating Implicity	146
	Getting into the Rhythm with Logarithmic Differentiation	148
	Differentiating Inverse Functions	149
	Scaling the Heights of Higher Order Derivatives	150
Chapter 11	Differentiation and the Shape of Curves	153
	Taking a Calculus Road Trip	153
	Finding Local Extrema--My Ma, She's Like, Totally Extreme	157
	Finding Absolute Extrema on a Closed Interval	163
	Finding Absolute Extrema over a Function's Entire Domain	166
	Locating Concavity and Inflection Points	168
	Looking at Graphs of Derivatives Till They Derive You Crazy	170
	The Mean Value Theorem--GRRRRR	174
Chapter 12	Your Problems Are Solved: Differentiation to the Rescue!	177
	Getting the Most (or Least) Out of Life: Optimization Problems	177
	Yo-Yo a Go-Go: Position, Velocity, and Acceleration	181
	Related Rates--They Rate, Relatively	189
	Tangents and Normals: Joined at the Hip	196
	Straight Shooting with Linear Approximations	201
	Business and Economics Problems	204
Part V	Integration and Infinite Series	209
Chapter 13	Intro to Integration and Approximating Area	211
	Integration: Just Fancy Addition	211
	Finding the Area under a Curve	214
	Dealing with Negative Area	216
	Approximating Area	216
	Getting Fancy with Summation Notation	224
	Finding Exact Area with the Definite Integral	228
	Approximating Area with the Trapezoid Rule and Simpson's Rule	231
Chapter 14	Integration: It's Backwards Differentiation	235
	Antidifferentiation--That's Differentiation in Reverse	235
	Vocabulary, Voshmabulary: What Difference Does It Make?	237
	The Annoying Area Function	237
	The Power and the Glory of the Fundamental Theorem of Calculus	240
	The Fundamental Theorem of Calculus: Take Two	244
	Finding Antiderivatives: Three Basic Techniques	251
	Finding Area with Substitution Problems	258
Chapter 15	Integration Techniques for Experts	261
	Integration by Parts: Divide and Conquer	261
	Tricky Trig Integrals	268
	Your Worst Nightmare: Trigonometric Substitution	274
	The As, Bs, and Cxs of Partial Fractions	279
Chapter 16	Forget Dr. Phil: Use the Integral to Solve Problems	285
	The Mean Value Theorem for Integrals and Average Value	286
	The Area between Two Curves--Double the Fun	289
	Finding the Volumes of Weird Solids	292
	Analyzing Arc Length	299
	Surfaces of Revolution--Pass the Bottle 'Round	301
	L'Hopital's Rule: Calculus for the Sick	304
	Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!	307
Chapter 17	Infinite Series	315
	Sequences and Series: What They're All About	316
	Convergence or Divergence? That Is the Question	321
	Alternating Series	332
	Keeping All the Tests Straight	336
Part VI	The Part of Tens	339
Chapter 18	Ten Things to Remember	341
	Your Sunglasses	341
	a[superscript 2] - b[superscript 2] = (a - b)(a + b)	341
	0/5 = 0, But 5/0 Is Undefined	341
	Anything[superscript 0] = 1	342
	SohCahToa	342
	Trigonometric Values for 30, 45, and 60 Degree Angles	342
	sin[superscript 2 theta] + cos[superscript 2 theta] = 1	343
	The Product Rule	343
	The Quotient Rule	343
	Where You Put Your Keys	343
Chapter 19	Ten Things to Forget	345
	(a + b)[superscript 2] = a[superscript 2] + b[superscript 2]--Wrong!	345
	[radical]a[superscript 2] + b[superscript 2] = a + b--Wrong!	345
	Slope = x[subscript 2] - x[subscript 1]/y[subscript 2] - y[subscript 1]--Wrong!	345
	3a + b/3a + c = b/c--Wrong!	346
	d/dx[pi superscript 3] = 3[pi superscript 2]--Wrong!	346
	If k Is a Constant, d/dx kx = k'x + kx'--Wrong!	346
	The Quotient Rule Is d/dx (u/v) = v'u - vu'/v[superscript 2]--Wrong!	346
	[function of] x[superscript 2] dx = 1/3x[superscript 3]--Wrong!	346
	[function of] (sinx) dx = cosx + C--Wrong!	347
	Green's Theorem	347
Chapter 20	Ten Things You Can't Get Away With	349
	Give Two Answers on Exam Questions	349
	Write Illegibly on Exams	349
	Don't Show Your Work on Exams	350
	Don't Do All of the Exam Problems	350
	Blame Your Study Partner for Your Low Exam Grade	350
	Tell Your Teacher That You Need an "A" in Calculus to Impress Your Significant Other	350
	Complain That Early-Morning Exams Are Unfair Because You're Not a "Morning Person"	351
	Protest the Whole Idea of Grades	351
	Pull the Fire Alarm During an Exam	351
	Use This Book as an Excuse	351
	Index	353