1. Analytic Geometry

1.1 Lines
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1.2 Distance Between Two Points; Circles
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1.3 Functions
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1.4 Shifts and Dilations
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2. Instantaneous Rate of Change: The Derivative

2.1 The slope of a function
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2.2 An example
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2.3 Limits
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2.4 The Derivative Function
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2.5 Adjectives For Functions
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3. Rules for Finding Derivatives

3.1 The Power Rule
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3.2 Linearity of the Derivative
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3.3 The Product Rule
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3.4 The Quotient Rule
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3.5 The Chain Rule
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4. Transcendental Functions

4.1 Trigonometric Functions
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4.2 The Derivative of sin x
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4.3 A hard limit
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4.4 The Derivative of sin x, continued
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4.5 Derivatives of the Trigonometric Functions
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4.6 Exponential and Logarithmic functions
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4.7 Derivatives of the exponential and logarithmic functions
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4.8 Implicit Differentiation
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4.9 Inverse Trigonometric Functions
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4.10 Limits revisited
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4.11 Hyperbolic Functions
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5. Curve Sketching

5.1 Maxima and Minima
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5.2 The first derivative test
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5.3 The second derivative test
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5.4 Concavity and inflection points
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5.5 Asymptotes and Other Things to Look For
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6. Applications of the Derivative

6.1 Optimization
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6.2 Related Rates
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6.3 Newton's Method
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6.4 Linear Approximations
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6.5 The Mean Value Theorem
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7. Integration

7.1 Two examples
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7.2 The Fundamental Theorem of Calculus
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7.3 Some Properties of Integrals
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8. Techniques of Integration

8.1 Substitution
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8.2 Powers of sine and cosine
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8.3 Trigonometric Substitutions
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8.4 Integration by Parts
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8.5 Rational Functions
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8.6 Numerical Integration
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8.7 Additional exercises
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9. Applications of Integration

9.1 Area between curves
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9.2 Distance, Velocity, Acceleration
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9.3 Volume
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9.4 Average value of a function
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9.5 Work
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9.6 Center of Mass
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9.7 Kinetic energy; improper integrals
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9.8 Probability
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9.9 Arc Length
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9.10 Surface Area
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10. Polar Coordinates, Parametric Equations

10.1 Polar Coordinates
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10.2 Slopes in polar coordinates
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10.3 Areas in polar coordinates
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10.4 Parametric Equations
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10.5 Calculus with Parametric Equations
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11. Sequences and Series

11.1 Sequences
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11.2 Series
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11.3 The Integral Test
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11.4 Alternating Series
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11.5 Comparison Tests
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11.6 Absolute Convergence
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11.7 The Ratio and Root Tests
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11.8 Power Series
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11.9 Calculus with Power Series
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11.10 Taylor Series
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11.11 Taylor's Theorem
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11.12 Additional exercises
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