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. Trigonometric 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. Implicit Differentiation
	7. Limits revisited
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
	4. Substitution
8. Applications of Integration
	1. Area between curves
	2. Distance, Velocity, Acceleration
	3. Volume
	4. Average value of a function
	5. Work
9. Transcendental Functions
	1. Inverse functions
	2. The natural logarithm
	3. The exponential function
	4. Other bases
	5. Inverse Trigonometric Functions
	6. Hyperbolic Functions
10. Techniques of Integration
	1. Powers of sine and cosine
	2. Trigonometric Substitutions
	3. Integration by Parts
	4. Rational Functions
	5. Numerical Integration
	6. Additional exercises
11. More Applications of Integration
	1. Center of Mass
	2. Kinetic energy; improper integrals
	3. Probability
	4. Arc Length
	5. Surface Area
12. 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
13. 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
14. Three Dimensions
	1. The Coordinate System
	2. Vectors
	3. The Dot Product
	4. The Cross Product
	5. Lines and Planes
	6. Other Coordinate Systems
15. Vector Functions
	1. Space Curves
	2. Calculus with vector functions
	3. Arc length and curvature
	4. Motion along a curve
16. Partial Differentiation
	1. Functions of Several Variables
	2. Limits and Continuity
	3. Partial Differentiation
	4. The Chain Rule
	5. Directional Derivatives
	6. Higher order derivatives
	7. Maxima and minima
	8. Lagrange Multipliers
17. Multiple Integration
	1. Volume and Average Height
	2. Double Integrals in Cylindrical Coordinates
	3. Moment and Center of Mass
	4. Surface Area
	5. Triple Integrals
	6. Cylindrical and Spherical Coordinates
	7. Change of Variables
18. Vector Calculus
	1. Vector Fields
	2. Line Integrals
	3. The Fundamental Theorem of Line Integrals
	4. Green's Theorem
	5. Divergence and Curl
	6. Vector Functions for Surfaces
	7. Surface Integrals
	8. Stokes's Theorem
	9. The Divergence Theorem
19. Differential Equations
	1. First Order Differential Equations
	2. First Order Homogeneous Linear Equations
	3. First Order Linear Equations
	4. Approximation
	5. Second Order Homogeneous Equations
	6. Second Order Linear Equations
	7. Second Order Linear Equations, take two
A. Selected Answers
B. Useful Formulas
Index