Numbers, Functions, and Graphs / Chapter 1: |
Introduction / 1-1: |
The Real Line and Coordinate Plane: Pythagoras / 1-2: |
Slopes and Equations of Straight Lines / 1-3: |
Circles and Parabolas: Descartes and Fermat / 1-4: |
The Concept of a Function / 1-5: |
Graphs of Functions / 1-6: |
Introductory Trigonometry / 1-7: |
The Functions Sin O and Cos O / 1-8: |
The Derivative of a Function / Chapter 2: |
What is Calculus ? / 2-0: |
The Problems of Tangents / 2-1: |
How to Calculate the Slope of the Tangent / 2-2: |
The Definition of the Derivative / 2-3: |
Velocity and Rates of Change: Newton and Leibriz / 2-4: |
The Concept of a Limit: Two Trigonometric Limits / 2-5: |
Continuous Functions: The Mean Value Theorem and Other Theorem / 2-6: |
The Computation of Derivatives / Chapter 3: |
Derivatives of Polynomials / 3-1: |
The Product and Quotient Rules / 3-2: |
Composite Functions and the Chain Rule / 3-3: |
Some Trigonometric Derivatives / 3-4: |
Implicit Functions and Fractional Exponents / 3-5: |
Derivatives of Higher Order / 3-6: |
Applications of Derivatives / Chapter 4: |
Increasing and Decreasing Functions: Maxima and Minima / 4-1: |
Concavity and Points of Inflection / 4-2: |
Applied Maximum and Minimum Problems / 4-3: |
More Maximum-Minimum Problems / 4-4: |
Related Rates / 4-5: |
Newtons Method for Solving Equations / 4-6: |
Applications to Economics: Marginal Analysis / 4-7: |
Indefinite Integrals and Differential Equations / Chapter 5: |
Differentials and Tangent Line Approximations / 5-1: |
Indefinite Integrals: Integration by Substitution / 5-3: |
Differential Equations: Separation of Variables / 5-4: |
Motion Under Gravity: Escape Velocity and Black Holes / 5-5: |
Definite Integrals / Chapter 6: |
The Problem of Areas / 6-1: |
The Sigma Notation and Certain Special Sums / 6-3: |
The Area Under a Curve: Definite Integrals / 6-4: |
The Computation of Areas as Limits / 6-5: |
The Fundamental Theorem of Calculus / 6-6: |
Properties of Definite Integrals / 6-7: |
Applications of Integration / Chapter 7: |
Introduction: The Intuitive Meaning of Integration / 7-1: |
The Area between Two Curves / 7-2: |
Volumes: The Disk Method / 7-3: |
Volumes: The Method of Cylindrical Shells / 7-4: |
Arc Length / 7-5: |
The Area of a Surface of Revolution / 7-6: |
Work and Energy / 7-7: |
Hydrostatic Force PART II / 7-8: |
Exponential and Logarithm Functions / Chapter 8: |
Review of Exponents and Logarithms / 8-1: |
The Number e and the Function y = e x / 8-3: |
The Natural Logarithm Function y = ln x / 8-4: |
Applications Population Growth and Radioactive Decay / 8-5: |
More Applications / 8-6: |
Trigonometric Functions / Chapter 9: |
Review of Trigonometry / 9-1: |
The Derivatives of the Sine and Cosine / 9-2: |
The Integrals of the Sine and Cosine / 9-3: |
The Derivatives of the Other Four Functions / 9-4: |
The Inverse Trigonometric Functions / 9-5: |
Simple Harmonic Motion / 9-6: |
Hyperbolic Functions / 9-7: |
Methods of Integration / Chapter 10: |
The Method of Substitution / 10-1: |
Certain Trigonometric Integrals / 10-3: |
Trigonometric Substitutions / 10-4: |
Completing the Square / 10-5: |
The Method of Partial Fractions / 10-6: |
Integration by Parts / 10-7: |
A Mixed Bag / 10-8: |
Numerical Integration / 10-9: |
Further Applications of Integration / Chapter 11: |
The Center of Mass of a Discrete System / 11-1: |
Centroids / 11-2: |
The Theorems of Pappus / 11-3: |
Moment of Inertia / 11-4: |
Indeterminate Forms and Improper Integrals / Chapter 12: |
Introduction. The Mean Value Theorem Revisited / 12-1: |
The Interminate Form 0/0. L'Hospital's Rule / 12-2: |
Other Interminate Forms / 12-3: |
Improper Integrals / 12-4: |
The Normal Distribution / 12-5: |
Infinite Series of Constants / Chapter 13: |
What is an Infinite Series ? / 13-1: |
Convergent Sequences / 13-2: |
Convergent and Divergent Series / 13-3: |
General Properties of Convergent Series / 13-4: |
Series on Non-negative Terms: Comparison Test / 13-5: |
Numbers, Functions, and Graphs / Chapter 1: |
Introduction / 1-1: |
The Real Line and Coordinate Plane: Pythagoras / 1-2: |