The humongous book of calculus problems Translated for people who don't speak math
Book - 2006
Saved in:
- Subjects
- Published
-
Indianapolis, IN :
Alpha
[2006]
- Language
- English
- Main Author
- Item Description
- "1,000 calculus problems with comprehensive solutions for all the major topics of calculus I and II"--Cover.
- Physical Description
- x, 565 pages : illustrations ; 28 cm
- Bibliography
- Includes index.
- ISBN
- 9781592575121
- Introduction
- Chapter 1. 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
- Chapter 2. 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
- Chapter 3. 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
- Chapter 4. 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
- Chapter 5. 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
- Chapter 6. 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
- Chapter 7. 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
- Chapter 8. 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
- Chapter 9. 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
- Chapter 10. 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
- Chapter 11. 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?
- Chapter 12. 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
- Chapter 13. 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?
- Chapter 14. 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
- Chapter 15. 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
- Chapter 16. 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!
- Chapter 17. 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
- Chapter 18. 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
- Chapter 19. 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
- Chapter 20. 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
- Chapter 21. 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
- Chapter 22. 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
- Chapter 23. 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
- Chapter 24. 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?
- Chapter 25. 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
- Chapter 26. 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
- Chapter 27. 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?
- Chapter 28. Advanced Infinite Series: Series that contain x's
- Power Series: Finding intervals of convergence
- Taylor and Maclaurin Series: Series that approximate function values
- Appendix A. Important Graphs to memorize and Graph Transformations
- Appendix B. The Unit Circle
- Appendix C. Trigonometric Identities
- Appendix D. Derivative Formulas
- Appendix E. Anti-Derivative Formulas
- Index