Calculus Students 2005 - 2006

Review and Preview 1. Functions and Their Graphs 2. Types of Functions; Shifting and Scaling 3. Graphing Calculators and Computers 4. Principles of Problem Solving 5. A Preview of Calculus

Limits and Rates of Change 6. The Tangent and Velocity Problem 7. The Limit of a Function 8. Calculating Limits Using Limit Properties 9. The Precise Definition of Limit 10. Continuity 11. Limits at Infinity; Horizontal Asymptotes 12. Tangents, Velocities, and Other Rates of Change

Derivatives 13. Differentiation Formulae 14. Rates of Change in the Natural and Social Sciences 15. Derivatives of Trigonometric Functions 16. The Chain Rule 17. Implicit Differentiation 18. Higher Derivatives 19. Related Rates 20. Differentials; Linear and Quadratic Approximations 21. Newton's Method

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 22. Exponential Functions and Their Derivatives 23. Inverse Functions 24. Logarithmic Functions 25. Derivatives of Logarithmic Functions 26. Exponential Growth and Decay 27. Inverse Trigonometric Functions 28. Hyperbolic Functions 29. Indeterminate Forms and L'Hopital's Rule

The Mean Value Theorem and Curve Sketching 30. Maximum and Minimum Values 31. The Mean Value Theorem 32. Monotonic Functions 33. Concavity and Points of Inflection 34. Curve Sketching 35. Graphing with Calculus and Calculators 36. Applied Maximum and Minimum Problems 37. Applications to Economics 38. Antiderivatives

Integrals 39. Sigma Notation 40. Area 41. The Definite Integral 42. The Fundamental Theorem of Calculus 43. The Substitution Method 44. The Logarithm Defined as an Integral

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