The Humongous Book of Calculus Problems

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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 Calculus has 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 ...

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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 Calculus has 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

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Product Details

  • ISBN-13: 9781592575121
  • Publisher: DK
  • Publication date: 1/2/2007
  • Pages: 576
  • Sales rank: 222,281
  • Product dimensions: 8.52 (w) x 10.82 (h) x 1.19 (d)

Meet the Author

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, which helps thousands of students conquer their math anxiety every month.
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Table of Contents

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

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  • Anonymous

    Posted February 15, 2008

    A reviewer

    If you found urself having a hard time reading or understanding ur cal textbook, this book would help u alot in terms of the language* and practice problems!! 5 star!

    2 out of 3 people found this review helpful.

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  • Posted December 11, 2012

    The detail inside is written with side chats and notes that help

    The detail inside is written with side chats and notes that help you follow thru. This is book is better for those that like more details and insight on how a problem was done. Like when teachers actually worked thru several problems in detail during class before the student would have to go home and struggle like they do today.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted September 24, 2009

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    Posted April 29, 2013

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    Posted November 23, 2010

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