The Humongous Book of Calculus Problems For People Who Don't Speak Math
, by Kelley, W. Michael
- ISBN: 9781592575121 | 1592575129
- Cover: Paperback
- Copyright: 1/2/2007
Now students have nothing to fear …Math textbooks can be as baffling as the subject they’re teaching. Not anymore. The best-selling author of The Complete Idiot’s Guide to Calculushas taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams. --Includes 1,000 problems with comprehensive solutions --Annotated notes throughout the text clarify what’s being asked in each problem and fill in missing steps --Kelley is a former award-winning calculus teacher
W. Michael Kelley is a former award-winning calculus teacher and author of The Complete Idiot-'s Guide to Calculus, The Complete Idiot-'s Guide to Precalculus, and The Complete Idiot-'s Guide to Algebra. He is also the founder and editor of calculus-help.com, which helps thousands of students conquer their math anxiety every month.
| Introduction | p. ix |
| Linear Equations and Inequalities: Problems containing x to the first power | p. 1 |
| Linear Geometry: Creating, graphing, and measuring lines and segments | p. 2 |
| Linear Inequalities and Interval Notation: Goodbye equal sign, hello parentheses and brackets | p. 5 |
| Absolute Value Equations and Inequalities: Solve two things for the price of one | p. 8 |
| Systems of Equations and Inequalities: Find a common solution | p. 11 |
| Polynomials: Because you can't have exponents of I forever | p. 15 |
| Exponential and Radical Expressions: Powers and square roots | p. 16 |
| Operations on Polynomial Expressions: Add, subtract, multiply, and divide polynomials | p. 18 |
| Factoring Polynomials: Reverse the multiplication process | p. 21 |
| Solving Quadratic Equations: Equations that have a highest exponent of 2 | p. 23 |
| Rational Expressions: Fractions, fractions, and more fractions | p. 27 |
| Adding and Subtracting Rational Expressions: Remember the least common denominator? | p. 28 |
| Multiplying and Dividing Rational Expressions: Multiplying = easy, dividing = almost as easy | p. 30 |
| Solving Rational Equations: Here comes cross multiplication | p. 33 |
| Polynomial and Rational Inequalities: Critical numbers break up your number line | p. 35 |
| Functions: Now you'll start seeing f(x) all over the place | p. 41 |
| Combining Functions: Do the usual (+,-,x,[divide]) or plug 'em into each other | p. 42 |
| Graphing Function Transformations: Stretches, squishes, flips, and slides | p. 45 |
| Inverse Functions: Functions that cancel other functions out | p. 50 |
| Asymptotes of Rational Functions: Equations of the untouchable dotted line | p. 53 |
| Logarithmic and Exponential Functions: Functions like log, x, lu x, 4x, and e[superscript x] | p. 57 |
| Exploring Exponential and Logarithmic Functions: Harness all those powers | p. 58 |
| Natural Exponential and Logarithmic Functions: Bases of e, and change of base formula | p. 62 |
| Properties of Logarithms: Expanding and sauishing log expressions | p. 63 |
| Solving Exponential and Logarithmic Equations: Exponents and logs cancel each other out | p. 66 |
| Conic Sections: Parabolas, circles, ellipses, and hyperbolas | p. 69 |
| Parabolas: Graphs of quadratic equations | p. 70 |
| Circles: Center + radius = round shapes and easy problems | p. 76 |
| Ellipses: Fancy word for "ovals" | p. 79 |
| Hyperbolas: Two-armed parabola-looking things | p. 85 |
| Fundamentals of Trigonometry: Inject sine, cosine, and tangent into the mix | p. 91 |
| Measuring Angles: Radians, degrees, and revolutions | p. 92 |
| Angle Relationships: Coterminal, complementary, and supplementary angles | p. 93 |
| Evaluating Trigonometric Functions: Right triangle trig and reference angles | p. 95 |
| Inverse Trigonometric Functions: Input a number and output an angle for a change | p. 102 |
| Trigonometric Graphs, Identities, and Equations: Trig equations and identity proofs | p. 105 |
| Graphing Trigonometric Transformations: Stretch and Shift wavy graphs | p. 106 |
| Applying Trigonometric Identities: Simplify expressions and prove identities | p. 110 |
| Solving Trigonometric Equations: Solve for [theta] instead of x | p. 115 |
| Investigating Limits: What height does the function intend to reach | p. 123 |
| Evaluating One-Sided and General Limits Graphically: Find limits on a function graph | p. 124 |
| Limits and Infinity: What happens when x or f(x) gets huge? | p. 129 |
| Formal Definition of the Limit: Epsilon-delta problems are no fun at all | p. 134 |
| Evaluating Limits: Calculate limits without a graph of the function | p. 137 |
| Substitution Method: As easy as plugging in for x | p. 138 |
| Factoring Method: The first thing to try if substitution doesn't work | p. 141 |
| Conjugate Method: Break this out to deal with troublesome radicals | p. 146 |
| Special Limit Theorems: Limit formulas you should memorize | p. 149 |
| Continuity and the Difference Quotient: Unbreakable graphs | p. 151 |
| Continuity: Limit exists + function defined = continuous | p. 152 |
| Types of Discontinuity: Hole vs. breaks, removable vs. nonremovable | p. 153 |
| The Difference Quotient: The "long way" to find the derivative | p. 163 |
| Differentiability: When does a derivative exist? | p. 166 |
| Basic Differentiation Methods: The four heavy hitters for finding derivatives | p. 169 |
| Trigonometric, Logarithmic, and Exponential Derivatives: Memorize these formulas | p. 170 |
| The Power Rule: Finally a shortcut for differentiating things like x[Prime] | p. 172 |
| The Product and Quotient Rules: Differentiate functions that are multiplied or divided | p. 175 |
| The Chain Rule: Differentiate functions that are plugged into functions | p. 179 |
| Derivatives and Function Graphs: What signs of derivatives tell you about graphs | p. 187 |
| Critical Numbers: Numbers that break up wiggle graphs | p. 188 |
| Signs of the First Derivative: Use wiggle graphs to determine function direction | p. 191 |
| Signs of the Second Derivative: Points of inflection and concavity | p. 197 |
| Function and Derivative Graphs: How are the graphs of f, f[prime], and f[Prime] related? | p. 202 |
| Basic Applications of Differentiation: Put your derivatives skills to use | p. 205 |
| Equations of Tangent Lines: Point of tangency + derivative = equation of tangent | p. 206 |
| The Extreme Value Theorem: Every function has its highs and lows | p. 211 |
| Newton's Method: Simple derivatives can approximate the zeroes of a function | p. 214 |
| L'Hopital's Rule: Find limits that used to be impossible | p. 218 |
| Advanced Applications of Differentiation: Tricky but interesting uses for derivatives | p. 223 |
| The Mean Rolle's and Rolle's Theorems: Average slopes = instant slopes | p. 224 |
| Rectilinear Motion: Position, velocity, and acceleration functions | p. 229 |
| Related Rates: Figure out how quickly the variables change in a function | p. 233 |
| Optimization: Find the biggest or smallest values of a function | p. 240 |
| Additional Differentiation Techniques: Yet more ways to differentiate | p. 247 |
| Implicit Differentiation: Essential when you can't solve a function for y | p. 248 |
| Logarithmic Differentiation: Use log properties to make complex derivatives easier | p. 255 |
| Differentiating Inverse Trigonometric Functions: 'Cause the derivative of tan[superscript -1] x ain't sec[superscript -2] x | p. 260 |
| Differentiating Inverse Functions: Without even knowing what they are! | p. 262 |
| Approximating Area: Estimating the area between a curve and the x-axiz | p. 269 |
| Informal Riemann Sums: Left, right, midpoint, upper, and lower sums | p. 270 |
| Trapezoidal Rule: Similar to Riemann sums but much more accurate | p. 281 |
| Simpson's Rule: Approximates area beneath curvy functions really well | p. 289 |
| Formal Riemann Sums: You'll want to poke your "i"s out | p. 291 |
| Integration: Now the derivative's not the answer, it's the question | p. 297 |
| Power Rule for Integration: Add I to the exponent and divide by the new power | p. 298 |
| Integrating Trigonometric and Exponential Functions: Trig integrals look nothing like trig derivatives | p. 301 |
| The Fundamental Theorem of Calculus: Integration and area are closely related | p. 303 |
| Substitution of Variables: Usually called u-substitution | p. 313 |
| Applications of the Fundamental Theorem: Things to do with definite integrals | p. 319 |
| Calculating the Area Between Two Curves: Instead of just a function and the x-axis | p. 320 |
| The Mean Value Theorem for Integration: Rectangular area matches the area beneath a curve | p. 326 |
| Accumulation Functions and Accumulated Change: Integrals with x limits and "real life" uses | p. 334 |
| Integrating Rational Expressions: Fractions inside the integral | p. 343 |
| Separation: Make one big ugly fraction into smaller, less ugly ones | p. 344 |
| Long Division: Divide before you integrate | p. 347 |
| Applying Inverse Trigonometric Functions: Very useful, but only in certain circumstances | p. 350 |
| Completing the Square: For quadratics down below and no variables up top | p. 353 |
| Partial Fractions: A fancy way to break down big fractions | p. 357 |
| Advanced Integration Techniques: Even more ways to find integrals | p. 363 |
| Integration by Parts: It's like the product rule, but for integrals | p. 364 |
| Trigonometric Substitution: Using identities and little right triangle diagrams | p. 368 |
| Improper Integrals: Integrating despite asymptotes and infinite boundaries | p. 383 |
| Cross-Sectional and Rotational Volume: Please put on your 3-D glasses at this time | p. 389 |
| Volume of a Solid with Known Cross-Sections: Cut the solid into pieces and measure those instead | p. 390 |
| Disc Method: Circles are the easiest possible cross-sections | p. 397 |
| Washer Method: Find volumes even if the "solids" aren't solid | p. 406 |
| Shell Method: Something to fall back on when the washer method fails | p. 417 |
| Advanced Applications of Definite Integrals: More bounded integral problems | p. 423 |
| Arc Length: How far is it from point A to point B along a curvy road? | p. 424 |
| Surface Area: Measure the "skin" of a rotational solid | p. 427 |
| Centroids: Find the center of gravity for a two-dimensional shape | p. 432 |
| Parametric and Polar Equations: Writing equations without x and y | p. 443 |
| Parametric Equations: Like revolutionaries in Boston Harbor, just add + | p. 444 |
| Polar Coordinates: Convert from (x,y) to (r, [theta]) and vice versa | p. 448 |
| Graphing Polar Curves: Graphing with r and [theta] instead of x and y | p. 451 |
| Applications of Parametric and Polar Differentiation: Teach a new dog some old differentiation tricks | p. 456 |
| Applications of Parametric and Polar Integration: Feed the dog some integrals too? | p. 462 |
| Differential Equations: Equations that contain a derivative | p. 467 |
| Separation of Variables: Separate the y's and dy's from the x's and dx's | p. 468 |
| Exponential Growth and Decay: When a population's change is proportional to its size | p. 473 |
| Linear Approximations: A graph and its tangent line sometimes look a lot alike | p. 480 |
| Slope Fields: They look like wind patterns on a weather map | p. 482 |
| Euler's Method: Take baby steps to find the differential equation's solution | p. 488 |
| Basic Sequences and Series: What's uglier than one fraction? Infinitely many | p. 495 |
| Sequences and Convergence: Do lists of numbers know where they're going? | p. 496 |
| Series and Basic Convergence Tests: Sigma notation and the nth term divergence test | p. 498 |
| Telescoping Series and p-Series: How to handle these easy-to-spot series | p. 502 |
| Geometric Series: Do they converge, and if so, what's the sum? | p. 505 |
| The Integral Test: Infinite series and improper integrals are related | p. 507 |
| Additional Infinite Series Convergence Tests: For use with uglier infinite series | p. 511 |
| Comparison Test: Proving series are bigger than big and smaller than small | p. 512 |
| Limit Comparison Test: Series that converge or diverge by association | p. 514 |
| Ratio Test: Compare neighboring terms of a series | p. 517 |
| Root Test: Helpful for terms inside radical signs | p. 520 |
| Alternating Series Test and Absolute Convergence: What if series have negative terms? | p. 524 |
| Advanced Infinite Series: Series that contain x's | p. 529 |
| Power Series: Finding intervals of convergence | p. 530 |
| Taylor and Maclaurin Series: Series that approximate function values | p. 538 |
| Important Graphs to memorize and Graph Transformations | p. 545 |
| The Unit Circle | p. 551 |
| Trigonometric Identities | p. 553 |
| Derivative Formulas | p. 555 |
| Anti-Derivative Formulas | p. 557 |
| Index | p. 559 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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