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