- 1. Functions, Limits, and Continuity
A review of the basics of functions is given. Students use linear approximations to study the limit process, before a more formal treatment of limits is given.
- 2. Derivatives
Students explore instantaneous rate of change, and the relationship between continuity and differentiability. The Chain Rule and implicit differentiation are reviewed.
- 3. Applications of Derivatives
Students gain practice with using the derivatives in related rates problems. Additional topics include The First Derivative Test, The Second Derivative Test, limits at infinity, optimization, and approximation errors.
- 4. Integration
Topics in this chapter include: indefinite integrals calculus, initial value problems, definite integrals, the Fundamental Theorem of Calculus, integration by substitution, and numerical integration.
- 5. Applications of Definite Integrals
This chapter includes applications of the definite integral, such as calculating areas between two curves, volumes, length of curves, and other real-world applications in physics and statistics.
- 6. Transcendental Functions
This chapter includes differentiation and integration of logarithmic and exponential functions, exponential growth and decay, derivatives and integrals involving inverse trigonometric functions, and L’Hospital’s Rule.
- 7. Integration Techniques
Topics in this chapter include: integration by substitution, integration by parts, integration by partial fractions, trigonometric integrals, trigonometric substitutions, and improper integrals.
- 8. Infinite Series
This chapter introduces the study of sequences and infinite series. The properties presented describe the behavior of a sequence or series, including whether a sequence approaches a number or an infinite series adds to a number.