Calculus demystified /
Steven G. Krantz
- 2nd
- New York: McGraw-Hill; 2011.
- 397 p.
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