| Introduction |
|
1 | (4) |
|
|
|
1 | (1) |
|
|
|
2 | (1) |
|
|
|
2 | (1) |
|
|
|
3 | (1) |
|
|
|
3 | (2) |
|
PART 1 PRE-CALCULUS REVIEW |
|
|
5 | (36) |
|
Chapter 1 Getting Down to Basics: Algebra and Geometry |
|
|
7 | (18) |
|
|
|
7 | (2) |
|
Misc. Algebra: You Know, Like Miss South Carolina |
|
|
9 | (2) |
|
Geometry: When Am I Ever Going to Need It? |
|
|
11 | (5) |
|
Solutions for This Easy, Elementary Stuff |
|
|
16 | (9) |
|
Chapter 2 Funky Functions and Tricky Trig |
|
|
25 | (16) |
|
Figuring Out Your Functions |
|
|
25 | (4) |
|
Trigonometric Calisthenics |
|
|
29 | (4) |
|
Solutions to Functions and Trigonometry |
|
|
33 | (8) |
|
PART 2 LIMITS AND CONTINUITY |
|
|
41 | (36) |
|
Chapter 3 A Graph Is Worth a Thousand Words: Limits and Continuity |
|
|
43 | (10) |
|
Digesting the Definitions: Limit and Continuity |
|
|
44 | (2) |
|
Taking a Closer Look: Limit and Continuity Graphs |
|
|
46 | (4) |
|
Solutions for Limits and Continuity |
|
|
50 | (3) |
|
Chapter 4 Nitty-Gritty Limit Problems |
|
|
53 | (24) |
|
Solving Limits with Algebra |
|
|
54 | (5) |
|
Pulling Out Your Calculator: Useful "Cheating" |
|
|
59 | (2) |
|
Making Yourself a Limit Sandwich |
|
|
61 | (2) |
|
Into the Great Beyond: Limits at Infinity |
|
|
63 | (4) |
|
Solutions for Problems with Limits |
|
|
67 | (10) |
|
|
|
77 | (114) |
|
Chapter 5 Getting the Big Picture: Differentiation Basics |
|
|
79 | (10) |
|
The Derivative: A Fancy Calculus Word for Slope and Rate |
|
|
79 | (2) |
|
The Handy-Dandy Difference Quotient |
|
|
81 | (3) |
|
Solutions for Differentiation Basics |
|
|
84 | (5) |
|
Chapter 6 Rules, Rules, Rules: The Differentiation Handbook |
|
|
89 | (28) |
|
|
|
89 | (3) |
|
Giving It Up for the Product and Quotient Rules |
|
|
92 | (2) |
|
Linking Up with the Chain Rule |
|
|
94 | (4) |
|
What to Do with Y's: Implicit Differentiation |
|
|
98 | (3) |
|
Getting High on Calculus: Higher Order Derivatives |
|
|
101 | (2) |
|
Solutions for Differentiation Problems |
|
|
103 | (14) |
|
Chapter 7 Analyzing Those Shapely Curves with the Derivative |
|
|
117 | (30) |
|
The First Derivative Test and Local Extrema |
|
|
117 | (3) |
|
The Second Derivative Test and Local Extrema |
|
|
120 | (2) |
|
Finding Mount Everest: Absolute Extrema |
|
|
122 | (4) |
|
Smiles and Frowns: Concavity and Inflection Points |
|
|
126 | (3) |
|
The Mean Value Theorem: Go Ahead, Make My Day |
|
|
129 | (2) |
|
Solutions for Derivatives and Shapes of Curves |
|
|
131 | (16) |
|
Chapter 8 Using Differentiation to Solve Practical Problems |
|
|
147 | (26) |
|
Optimization Problems: From Soup to Nuts |
|
|
147 | (3) |
|
Problematic Relationships: Related Rates |
|
|
150 | (3) |
|
A Day at the Races: Position, Velocity, and Acceleration |
|
|
153 | (4) |
|
Solutions to Differentiation Problem Solving |
|
|
157 | (16) |
|
Chapter 9 Even More Practical Applications of Differentiation |
|
|
173 | (18) |
|
Make Sure You Know Your Lines: Tangents and Normals |
|
|
173 | (4) |
|
Looking Smart with Linear Approximation |
|
|
177 | (2) |
|
Calculus in the Real World: Business and Economics |
|
|
179 | (4) |
|
Solutions to Differentiation Problem Solving |
|
|
183 | (8) |
|
PART 4 INTEGRATION AND INFINITE SERIES |
|
|
191 | (118) |
|
Chapter 10 Getting into Integration |
|
|
193 | (20) |
|
Adding Up the Area of Rectangles: Kid Stuff |
|
|
193 | (3) |
|
Sigma Notation and Riemann Sums: Geek Stuff |
|
|
196 | (4) |
|
Close Isn't Good Enough: The Definite Integral and Exact Area |
|
|
200 | (2) |
|
Finding Area with the Trapezoid Rule and Simpson's Rule |
|
|
202 | (3) |
|
Solutions to Getting into Integration |
|
|
205 | (8) |
|
Chapter 11 Integration: Reverse Differentiation |
|
|
213 | (16) |
|
The Absolutely Atrocious and Annoying Area Function |
|
|
213 | (3) |
|
Sound the Trumpets: The Fundamental Theorem of Calculus |
|
|
216 | (3) |
|
Finding Antiderivatives: The Guess-and-Check Method |
|
|
219 | (2) |
|
The Substitution Method: Pulling the Switcheroo |
|
|
221 | (4) |
|
Solutions to Reverse Differentiation Problems |
|
|
225 | (4) |
|
Chapter 12 Integration Rules for Calculus Connoisseurs |
|
|
229 | (26) |
|
Integration by Parts: Here's How u du It |
|
|
229 | (4) |
|
Transfiguring Trigonometric Integrals |
|
|
233 | (2) |
|
Trigonometric Substitution: It's Your Lucky Day! |
|
|
235 | (2) |
|
Partaking of Partial Fractions |
|
|
237 | (4) |
|
Solutions for Integration Rules |
|
|
241 | (14) |
|
Chapter 13 Who Needs Freud? Using the Integral to Solve Your Problems |
|
|
255 | (22) |
|
Finding a Function's Average Value |
|
|
255 | (1) |
|
Finding the Area between Curves |
|
|
256 | (2) |
|
Volumes of Weird Solids: No, You're Never Going to Need This |
|
|
258 | (7) |
|
Arc Length and Surfaces of Revolution |
|
|
265 | (3) |
|
Solutions to Integration Application Problems |
|
|
268 | (9) |
|
Chapter 14 Infinite (Sort of) Integrals |
|
|
277 | (10) |
|
Getting Your Hopes Up with L'Hopital's Rule |
|
|
278 | (2) |
|
Disciplining Those Improper Integrals |
|
|
280 | (3) |
|
Solutions to Infinite (Sort of) Integrals |
|
|
283 | (4) |
|
Chapter 15 Infinite Series: Welcome to the Outer Limits |
|
|
287 | (22) |
|
|
|
287 | (2) |
|
Testing Three Basic Series |
|
|
289 | (2) |
|
Apples and Oranges ... and Guavas: Three Comparison Tests |
|
|
291 | (4) |
|
Ratiocinating the Two "R" Tests |
|
|
295 | (2) |
|
He Loves Me, He Loves Me Not: Alternating Series |
|
|
297 | (2) |
|
Solutions to Infinite Series |
|
|
299 | (10) |
|
|
|
309 | (10) |
|
Chapter 16 Ten Things about Limits, Continuity, and Infinite Series |
|
|
311 | (4) |
|
|
|
311 | (2) |
|
First 3 over the "1": 3 parts to the definition of a limit |
|
|
312 | (1) |
|
Fifth 3 over the "1": 3 cases where a limit fails to exist |
|
|
312 | (1) |
|
Second 3 over the "1": 3 parts to the definition of continuity |
|
|
312 | (1) |
|
Fourth 3 over the "1": 3 cases where continuity fails to exist |
|
|
312 | (1) |
|
Third 3 over the "m": 3 cases where a derivative fails to exist |
|
|
313 | (1) |
|
|
|
313 | (2) |
|
First 1: The nth term test of divergence |
|
|
313 | (1) |
|
Second 1: The nth term test of convergence for alternating series |
|
|
313 | (1) |
|
First 3: The three tests with names |
|
|
313 | (1) |
|
Second 3: The three comparison tests |
|
|
314 | (1) |
|
The 2 in the middle: The two R tests |
|
|
314 | (1) |
|
Chapter 17 Ten Things You Better Remember about Differentiation |
|
|
315 | (4) |
|
|
|
315 | (1) |
|
The First Derivative Is a Rate |
|
|
315 | (1) |
|
The First Derivative Is a Slope |
|
|
316 | (1) |
|
Extrema, Sign Changes, and the First Derivative |
|
|
316 | (1) |
|
The Second Derivative and Concavity |
|
|
316 | (1) |
|
Inflection Points and Sign Changes in the Second Derivative |
|
|
316 | (1) |
|
|
|
317 | (1) |
|
|
|
317 | (1) |
|
|
|
317 | (1) |
|
"PSST," Here's a Good Way to Remember the Derivatives of Trig Functions |
|
|
317 | (2) |
| Index |
|
319 | |
Daugiau apie elektronines knygas