Includes index.

pt. I. An overview of calculus -- 1. What is calculus? -- 2. The two big ideas of calculus : differentiation and integration-- Slope -- Rate -- Plus infinite series -- Divergent series -- Convergent series -- 3. Why calculus works -- The limit concept : a mathematical microscope -- Precision -- Infinity --

pt. II. Warming up with calculus prerequisites -- 4. Pre-algebra and algebra review -- Fractions -- Multiplying fractions -- Dividing fractions -- Adding fractions -- Subtracting fractions -- Canceling in fractions -- Absolute value -- Powers -- Roots -- Simplifying roots -- Logarithms -- Factoring -- GCF -- Trinomial factoring -- Solving quadratic equations -- Factoring -- The quadratic formula -- Completing the square -- 5. Funky functions and their groovy graphs -- Independent and dependent variables -- Function notation -- Composite functions -- Common functions and their graphs -- Lines in the plane -- Parabolic and absolute value functions -- Couple oddball functions -- Exponential functions -- Logarithmic functions -- Inverse functions -- Horizontal transformations -- Vertical transformations -- 6. The trig tango -- Right triangles -- Unit circle -- Measuring angles with radians -- Hypotenuse -- Graphing sine, cosine, and tangent -- Inverse trig functions -- Trig identities --

pt. III. Limits -- 7. Limits and continuity -- One-sided limits -- Limits and vertical asymptotes -- Limits and horizontal asymptotes -- Calculating instantaneous speed with limits -- Linking limits and continuity -- 8. Evaluating limits -- Figuring a limit with your calculator -- Solving limit problems with algebra -- Evaluating limits at infinity -- Limits at infinity and horizontal asymptotes -- Solving limits at infinity with a calculator -- Solving limits at infinity with algebra --

pt. IV. Differentiation -- 9. Differentiation orientation -- The slope off a line -- The derivative of a line -- The derivative : it's just a rate -- Calculus on the playground -- Speed -- The rate-slope connection -- The derivative of a curve -- The difference quotient -- Average rate and instantaneous rate -- 10. Differentiation rules : yeah, man, it rules -- Basic differentiation rules -- The constant rule -- The power rule -- The constant multiple rule -- The sum rule -- The difference rule -- Differentiating trig functions -- Differentiating exponential and logarithmic functions -- The product rule -- The quotient rule -- The chain rule -- Differentiating implicitly -- Logarithmic differentiation -- Differentiating inverse functions -- Higher order derivatives -- 11. Differentiation and the shape of curves -- Positive and negative slopes -- Concavity and inflection points -- A local minimum -- The absolute maximum -- Finding local extrema -- Critical numbers -- Finding absolute extrema on a closed interval -- Finding absolute extrema over a function's entire domain -- Locating concavity and inflection points -- Graphs of derivatives -- The mean value theorem -- 12. Your problems are solved : differentiation to the rescue! -- Optimization problems -- Maximum volume of a box -- Maximum area of a corral -- Position, velocity, and acceleration -- Velocity, speed and acceleration -- Maximum and minimum height -- Velocity and displacement -- Speed and distance traveled -- Related rates -- 13. More differentiation problems : going off on a tangent -- Tangents and normals -- The tangent line problem -- The normal line problem -- Linear approximations -- Business and economics problems -- Managing marginals in economics --

pt. V. Integration and infinite series -- 14. Intro to integration and approximating area -- Integration : just fancy addition -- Finding the area under a curve -- Approximating area -- Left sums -- Right sums -- Midpoint sums -- Summation notation -- Riemann sums with sigma notation -- Finding exact area with the definite integral -- Trapezoid rule and Simpson's rule (Thomas Simpson 1710-1761) -- 15. Integration : it's backwards differentiation -- Antidifferentiation -- Area function -- Fundamental theorem of calculus -- Antiderivatives -- Finding area with substitution problems -- 16. Integration techniques for experts -- Integration by parts -- Trig integrals -- Integrals containing sines and cosines -- Integrals containing secants and tangents or cosecants -- Trigonometric substitution -- Partial fractions -- 17. Forget Dr. Phil : use the integral to solve problems -- The mean value theorem for integrals and average value -- The area between two curves -- Finding the volumes of weird solids -- Analyzing arc length -- Surfaces of revolution -- 18. Taming the infinite with improper integrals -- L/Hôpital's rule -- Improper integrals -- Improper integrals with vertical asymptotes -- Improper integrals with one or two infinite limits of integration -- 19. Infinite series -- Sequences and series -- Stringing sequences -- Summing series -- Convergence or divergence -- Alternating series --

pt. VI. The part of tens -- 20. Ten things to remember -- The product rule -- The quotient rule -- 21. Ten things to forget -- 22. Ten things you can't get away with.