Contents
Introduction
1. Analytic Geometry
	1. Lines
	2. Distance Between Two Points; Circles
	3. Functions
	4. Shifts and Dilations
2. Instantaneous Rate of Change: The Derivative
	1. The slope of a function
	2. An example
	3. Limits
	4. The Derivative Function
	5. Properties of Functions
3. Rules for Finding Derivatives
	1. The Power Rule
	2. Linearity of the Derivative
	3. The Product Rule
	4. The Quotient Rule
	5. The Chain Rule
4. Transcendental Functions
	1. Trigonometric Functions
	2. The Derivative of the sine
	3. A hard limit
	4. The Derivative of the sine, continued
	5. Derivatives of the Trigonometric Functions
	6. Exponential and Logarithmic functions
	7. Derivatives of the exponential and logarithmic functions
	8. Implicit Differentiation
	9. Inverse Trigonometric Functions
	10. Limits revisited
	11. Hyperbolic Functions
5. Curve Sketching
	1. Maxima and Minima
	2. The first derivative test
	3. The second derivative test
	4. Concavity and inflection points
	5. Asymptotes and Other Things to Look For
6. Applications of the Derivative
	1. Optimization
	2. Related Rates
	3. Newton's Method
	4. Linear Approximations
	5. The Mean Value Theorem
7. Integration
	1. Two examples
	2. The Fundamental Theorem of Calculus
	3. Some Properties of Integrals
8. Techniques of Integration
	1. Substitution
	2. Powers of sine and cosine
	3. Trigonometric Substitutions
	4. Integration by Parts
	5. Rational Functions
	6. Numerical Integration
	7. Additional exercises
9. Applications of Integration
	1. Area between curves
	2. Distance, Velocity, Acceleration
	3. Volume
	4. Average value of a function
	5. Work
	6. Center of Mass
	7. Kinetic energy; improper integrals
	8. Probability
	9. Arc Length
	10. Surface Area
10. Polar Coordinates, Parametric Equations
	1. Polar Coordinates
	2. Slopes in polar coordinates
	3. Areas in polar coordinates
	4. Parametric Equations
	5. Calculus with Parametric Equations
11. Sequences and Series
	1. Sequences
	2. Series
	3. The Integral Test
	4. Alternating Series
	5. Comparison Tests
	6. Absolute Convergence
	7. The Ratio and Root Tests
	8. Power Series
	9. Calculus with Power Series
	10. Taylor Series
	11. Taylor's Theorem
	12. Additional exercises
A. Selected Answers
B. Useful Formulas
Index