Difference between revisions of "AP Calculus"
(→Course Content) |
m (→Course Content) |
||
| Line 10: | Line 10: | ||
**Properties of limits | **Properties of limits | ||
**Limits at infinity | **Limits at infinity | ||
| + | **L'Hôpital's rule (will be added to AB in 2017) | ||
*Continuity | *Continuity | ||
**Showing a function is continuous at a point | **Showing a function is continuous at a point | ||
| Line 43: | Line 44: | ||
**Volumes of cross sections | **Volumes of cross sections | ||
**Solids of revolution | **Solids of revolution | ||
| + | |||
| + | AP Calculus BC covers everything found in AB, plus the following topics: | ||
| + | |||
| + | *Sequences | ||
| + | **Arithmetic sequences defined recursively and explicitly | ||
| + | **Geometric sequences defined recursively and explicitly | ||
| + | **Oscillating sequences | ||
| + | **Limits at infinity | ||
| + | **L'Hôpital's rule (will also be covered in AB in 2017 exam) | ||
| + | *Series | ||
| + | **Finite arithmetic and geometric series | ||
| + | **Infinite and power series | ||
| + | **Maclaurin and Taylor series | ||
| + | *Parameterization | ||
| + | *Polar coordinates | ||
| + | *Vectors in the 2-dimensional place | ||
Revision as of 14:36, 3 March 2016
AP Calculus, or Advanced Placement Calculus, refers to the two Advanced Placement Calculus courses run by the College Board. The two courses are AP Calculus AB and AP Calculus BC. AP Calculus AB is supposed to be roughly equal to the first semester and a half of a typical year-long introductory, single-variable college calculus course, while AP Calculus BC is allegedly equal to the full year. Students may take the AP Calculus AB or BC exam administered every year in May for potential college credit. Like all other AP courses, students need not to actually take the class; they may take just the exam for possible college credit.
Course Content
The AP Calculus AB covers the following topics:
- Limits
- Rational functions
- Trigonometric, logarithmic, and exponential limits
- Properties of limits
- Limits at infinity
- L'Hôpital's rule (will be added to AB in 2017)
- Continuity
- Showing a function is continuous at a point
- Differentiation
- Definition of derivative
- Linear differentiation rules
- Product, quotient, and chain rule
- Trigonometric, exponential, and logarithmic functions
- Logarithmic differentiation
- Second and higher order differentiation
- Applications of the derivative
- Mean Value Theorem, Intermediate Value Theorem, and Extreme Value Theorem (MVT, IVT, EVT)
- Optimization and Related Rates
- Linear approximation
- Concavity
- Relationship to position, velocity, and acceleration
- Integration
- Properties of integration
- Fundamental Theorem of Calculus
- Indefinite Integrals
substitution (reverse chain rule)- Partial fraction decomposition
- Integration by parts
- Improper Integrals
- First order differential equations
- Modeling exponential growth/decay with differential equations
- Separable differential equations
- Euler's method
- Applications of the definite integral
- Net change
- Relationship to position, velocity, and acceleration
- Areas in the plane
- Volumes of cross sections
- Solids of revolution
substitution (reverse chain rule)AP Calculus BC covers everything found in AB, plus the following topics:
- Sequences
- Arithmetic sequences defined recursively and explicitly
- Geometric sequences defined recursively and explicitly
- Oscillating sequences
- Limits at infinity
- L'Hôpital's rule (will also be covered in AB in 2017 exam)
- Series
- Finite arithmetic and geometric series
- Infinite and power series
- Maclaurin and Taylor series
- Parameterization
- Polar coordinates
- Vectors in the 2-dimensional place
