Humongous Book of Calculus Problems

ISBN-10: 1592575129
ISBN-13: 9781592575121
Edition: 2006
List price: $21.95 Buy it from $8.73
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Description: Now students have nothing to fear Math textbooks can be as baffling as the subject theyre teaching. Not anymore. The best-selling author of The Complete Idiots Guide to Calculushas taken what appears to be a typical calculus workbook, chock full of  More...

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Book details

List price: $21.95
Copyright year: 2006
Publisher: Dorling Kindersley Publishing, Incorporated
Publication date: 1/2/2007
Binding: Paperback
Pages: 512
Size: 8.25" wide x 10.00" long x 1.25" tall
Weight: 2.596
Language: English

Now students have nothing to fear Math textbooks can be as baffling as the subject theyre teaching. Not anymore. The best-selling author of The Complete Idiots 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 whats being asked in each problem and fill in missing steps --Kelley is a former award-winning calculus teacher

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

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