Calculus For Dummies, 2nd Edition

Calculus For Dummies, 2nd Edition (9781118791295) Is Now Being Published As Calculus For Dummies, 2nd Edition (9781119293491). While This Version Features An Older Dummies Cover And Design, The Content Is The Same As The New Release And Should Not Be Considered A Different Product. Slay The Calculus Monster With This User-friendly Guide Calculus For Dummies, 2nd Edition Makes Calculus Manageable—even If You're One Of The Many Students Who Sweat At The Thought Of It. By Breaking Down Differentiation And Integration Into Digestible Concepts, This Guide Helps You Build A Stronger Foundation With A Solid Understanding Of The Big Ideas At Work. This User-friendly Math Book Leads You Step-by-step Through Each Concept, Operation, And Solution, Explaining The How And Why In Plain English Instead Of Math-speak. Through Relevant Instruction And Practical Examples, You'll Soon Learn That Real-life Calculus Isn't Nearly The Monster It's Made Out To Be. Calculus Is A Required Course For Many College Majors, And For Students Without A Strong Math Foundation, It Can Be A Real Barrier To Graduation. Breaking That Barrier Down Means Recognizing Calculus For What It Is—simply A Tool For Studying The Ways In Which Variables Interact. It's The Logical Extension Of The Algebra, Geometry, And Trigonometry You've Already Taken, And Calculus For Dummies, 2nd Edition Proves That If You Can Master Those Classes, You Can Tackle Calculus And Win. Includes Foundations In Algebra, Trigonometry, And Pre-calculus Concepts Explores Sequences, Series, And Graphing Common Functions Instructs You How To Approximate Area With Integration Features Things To Remember, Things To Forget, And Things You Can't Get Away With Stop Fearing Calculus, And Learn To Embrace The Challenge. With This Comprehensive Study Guide, You'll Gain The Skills And Confidence That Make All The Difference. Calculus For Dummies, 2nd Edition Provides A Roadmap For Success, And The Backup You Need To Get There. 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. Calculus For Dummies, 2nd Edition makes calculus manageable - even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. 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.