Calculus for dummies
By: by Mark Ryan, founder of the Math Center
Edition: 2nd edition.
Series: ---For dummies; --For dummies
Published: 2014
Language: eng
Number of pages: 370
ISBN-13: 9781118791295
Subjects: Calculus
Description: This hands-on guide makes calculus manageable-- even if it makes you sweat! Ryan leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English.
Notes: Includes index.
Table of contents: title: pt. I. An overview of calculus; title: 1. What is calculus?; title: 2. The two big ideas of calculus : differentiation and integration; title: Slope; title: Rate; title: Plus infinite series; title: Divergent series; title: Convergent series; title: 3. Why calculus works; title: The limit concept : a mathematical microscope; title: Precision; title: Infinity; title: pt. II. Warming up with calculus prerequisites; title: 4. Pre-algebra and algebra review; title: Fractions; title: Multiplying fractions; title: Dividing fractions; title: Adding fractions; title: Subtracting fractions; title: Canceling in fractions; title: Absolute value; title: Powers; title: Roots; title: Simplifying roots; title: Logarithms; title: Factoring; title: GCF; title: Trinomial factoring; title: Solving quadratic equations; title: Factoring; title: The quadratic formula; title: Completing the square; title: 5. Funky functions and their groovy graphs; title: Independent and dependent variables; title: Function notation; title: Composite functions; title: Common functions and their graphs; title: Lines in the plane; title: Parabolic and absolute value functions; title: Couple oddball functions; title: Exponential functions; title: Logarithmic functions; title: Inverse functions; title: Horizontal transformations; title: Vertical transformations; title: 6. The trig tango; title: Right triangles; title: Unit circle; title: Measuring angles with radians; title: Hypotenuse; title: Graphing sine, cosine, and tangent; title: Inverse trig functions; title: Trig identities; title: pt. III. Limits; title: 7. Limits and continuity; title: One-sided limits; title: Limits and vertical asymptotes; title: Limits and horizontal asymptotes; title: Calculating instantaneous speed with limits; title: Linking limits and continuity; title: 8. Evaluating limits; title: Figuring a limit  with your calculator; title: Solving limit problems with algebra; title: Evaluating limits at infinity; title: Limits at infinity and horizontal asymptotes; title: Solving limits at infinity with a calculator; title: Solving limits at infinity with algebra; title: pt. IV. Differentiation; title: 9. Differentiation orientation; title: The slope off a line; title: The derivative of a line; title: The derivative : it's just a rate; title: Calculus on the playground; title: Speed; title: The rate-slope connection; title: The derivative of a curve; title: The difference quotient; title: Average rate and instantaneous rate; title: 10. Differentiation rules : yeah, man, it rules; title: Basic differentiation rules; title: The constant rule; title: The power rule; title: The constant multiple rule; title: The sum rule; title: The difference rule; title: Differentiating trig functions; title: Differentiating exponential and logarithmic functions; title: The product rule; title: The quotient rule; title: The chain rule; title: Differentiating implicitly; title: Logarithmic differentiation; title: Differentiating inverse functions; title: Higher order derivatives; title: 11. Differentiation and the shape of curves; title: Positive and negative slopes; title: Concavity and inflection points; title: A local minimum; title: The absolute maximum; title: Finding local extrema; title: Critical numbers; title: Finding absolute extrema on a closed interval; title: Finding absolute extrema over a function's entire domain; title: Locating concavity and inflection points; title: Graphs of derivatives; title: The mean value theorem; title: 12. Your problems are solved : differentiation to the rescue!; title: Optimization problems; title: Maximum volume of a box; title: Maximum area of a corral; title: Position, velocity, and acceleration; title: Velocity, speed and acceleration; title: Maximum and minimum height; title: Velocity and displacement; title: Speed and distance traveled; title: Related rates; title: 13. More differentiation problems : going off on a tangent; title: Tangents and normals; title: The tangent line problem; title: The normal line problem; title: Linear approximations; title: Business and economics problems; title: Managing marginals in economics; title: pt. V. Integration and infinite series; title: 14. Intro to integration and approximating area; title: Integration : just fancy addition; title: Finding the area under a curve; title: Approximating area; title: Left sums; title: Right sums; title: Midpoint sums; title: Summation notation; title: Riemann sums with sigma notation; title: Finding exact area with the definite integral; title: Trapezoid rule and Simpson's rule (Thomas Simpson 1710-1761); title: 15. Integration : it's backwards differentiation; title: Antidifferentiation; title: Area function; title: Fundamental theorem of calculus; title: Antiderivatives; title: Finding area with substitution problems; title: 16. Integration techniques for experts; title: Integration by parts; title: Trig integrals; title: Integrals containing sines and cosines; title: Integrals containing secants and tangents or cosecants; title: Trigonometric substitution; title: Partial fractions; title: 17. Forget Dr. Phil : use the integral to solve problems; title: The mean value theorem for integrals and average value; title: The area between two curves; title: Finding the volumes of weird solids; title: Analyzing arc length; title: Surfaces of revolution; title: 18. Taming the infinite with improper integrals; title: L/Hôpital's rule; title: Improper integrals; title: Improper integrals with vertical asymptotes; title: Improper integrals with one or two infinite limits of integration; title: 19. Infinite series; title: Sequences and series; title: Stringing sequences; title: Summing series; title: Convergence or divergence; title: Alternating series; title: pt. VI. The part of tens; title: 20. Ten things to remember; title: The product rule; title: The quotient rule; title: 21. Ten things to forget; title: 22. Ten things you can't get away with.