Ebook: Calculus Demystified

"Calculate this: learning calculus just got a whole lot easier! Stumped trying to understand calculus? Calculus demystified, second edition, will help you master this essential mathematical subject. Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts. It's a no-brainer! You'll get: applications of the derivative and the integral rules of integration coverage of improper integrals An explanation of calculus with logarithmic and exponential functions dtails on calculation of work, averages, arc length, and surface area Simple enough for a beginner, but challenging enough for an advanced student, Calculus demystified, second edition, is one book you won't want to function without!"--Provided by publisher."More than 1.8 million books sold in the DeMYSTiFieD series! The second edition of this bestseller is updated with all-new quizzes and test questions, clearer explanations of the exercises, and a completely refreshed design"--Provided by publisher.  Read more...
Preface --
How to use this book --
Chapter 1: Basics --
1-0: Introductory remarks --
1-1: Number systems --
1-2: Coordinates in one dimension --
1-3: Coordinates in two dimensions --
1-4: Slope of a line in the plane --
1-5: Equation of a line --
1-6: Loci in the plane --
1-7: Trigonometry --
1-8: Sets and functions --
1-8-1: Examples of functions of a real variable --
1-8-2: Graphs of functions --
1-8-3: Plotting the graph of a function --
1-8-4: Composition of functions --
1-8-5: Inverse of a function --
1-9: Few words about logarithms and exponentials --
Quiz --
Chapter 2: Foundations Of Calculus --
2-1: Limits --
2-1-1: One-sided limits --
2-2: Properties of limits --
2-3: Continuity --
2-4: Derivative --
2-5: Rules for calculating derivatives --
2-5-1: Derivative of an inverse --
2-6: Derivative as a rate of change --
Quiz --
Chapter 3: Applications Of The Derivative --
3-1: Graphing of functions --
3-2: Maximum/minimum problems --
3-3: Related rates --
3-4: Falling bodies --
Quiz --
Chapter 4: Integral --
4-0: Introduction --
4-1: Antiderivatives and indefinite integrals --
4-1-1: Concept of antiderivative --
4-1-2: Indefinite integral --
4-2: Area --
4-3: Signed area --
4-4: Area between two curves --
4-5: Rules of integration --
4-5-1: Linear properties --
4-5-2: Additivity --
Quiz --
Chapter 5: Indeterminate Forms --
5-1: I'Hopital's Rule --
5-1-1: Introduction --
5-1-2: I'Hopital's Rule --
5-2: Other indeterminate forms --
5-2-1: Introduction --
5-2-2: Writing a product as a quotient --
5-2-3: Use of the logarithm --
5-2-4: Putting terms over a common denominator --
5-2-5: Other algebraic manipulations --
5-3: Improper integrals: a first look --
5-3-1: Introduction --
5-3-2: Integrals with infinite integrands --
5-3-3: Application to area --
5-4: More on improper integrals --
5-4-1: Introduction --
5-4-2: Integral on an infinite interval --
5-4-3: Some applications --
Quiz --
Chapter 6: Transcendental Functions --
6-0: Introductory remarks --
6-1: Logarithm basics --
6-1-1: New approach to logarithms --
6-1-2: Logarithm function and the derivative --
6-2: Exponential basics --
6-2-1: Facts about the exponential function --
6-2-2: Calculus properties of the exponential --
6-2-3: Number e --
6-3: Exponentials with arbitrary bases --
6-3-1: Arbitrary powers --
6-3-2: Logarithms with arbitrary bases --
6-4: Calculus with logs and exponentials to arbitrary bases --
6-4-1: Differentiation and integration of log(a)x and a(x) --
6-4-2: Graphing of logarithmic and exponential functions --
6-4-3: Logarithmic differentiation --
6-5: Exponential growth and decay --
6-5-1: Differential equation --
6-5-2: Bacterial growth --
6-5-3: Radioactive decay --
6-5-4: Compound interest --
6-6: Inverse trigonometric functions --
6-6-1: Introductory remarks --
6-6-2: Inverse sine and cosine --
6-6-3: Inverse tangent function --
6-6-4: Integrals in which inverse trigonometric functions arise --
6-6-5: Other inverse trigonometric functions --
6-6-6: Example involving inverse trigonometric functions --
Quiz --
Chapter 7: Methods Of Integration --
7-1: Integration by parts --
7-2: Partial fractions --
7-2-1: Introductory remarks --
7-2-2: Products of linear factors --
7-2-3: Quadratic factors --
7-3: Substitution --
7-4: Integrals of trigonometric expressions --
Quiz --
Chapter 8: Applications Of The Integral --
8-1: Volumes by slicing --
8-1-0: Introduction --
8-1-1: Basic strategy --
8-1-2: Examples --
8-2: Volumes of solids of revolution --
8-2-0: Introduction --
8-2-1: Method of washers --
8-2-2: Method of cylindrical shells --
8-2-3: Different axes --
8-3: Work --
8-4: Averages --
8-5: Arc length and surface area --
8-5-1: Arc length --
8-5-2: Surface area --
8-6: Hydrostatic pressure --
8-7: Numerical methods of integration --
8-7-1: Trapezoid rule --
8-7-2: Simpson's rule --
Quiz --
Final exam --
Answers to quizzes and final exam --
Bibliography --
Index.