AP/Advanced Calculus Part 3 prepares students for the BC part of the AP Calculus exam and meets the Advanced Placement criteria required by the College Board. AP/Advanced Calculus Part 3 builds on the concepts learned in AP/Advanced Calculus Parts 1 and 2. Students will study limits in indeterminate forms, L'Hôpital's Rule, growth rates of functions, and indefinite integrals. Also, students will study a variety of sequences and series, polynomials of infinite degree, and their derivatives and integrals. Taylor series and MacClaurin series, as well as tests for convergence and divergence, will be covered. The course closes with parametric functions, vectors, and polar coordinates.
It is recommended that students successfully complete AP/Advanced Calculus Parts 1 and 2 or equivalent course work before enrolling in this course.
Course Objectives
Unit 1: Essential Content and Skills
- Evaluate integrals by parts and by tabular integration.
- Apply concepts of local linearity by using Euler’s Method.
- Integrate with partial fractions.
- Determine whether a sequence diverges or converges.
- Examine L’Hôpital’s Rule to evaluate limits.
- Evaluate integrals with infinite discontinuities.
- Determine if an improper integral converges or diverges.
Unit 2: Essential Content and Skills
- Evaluate integrals with infinite discontinuities.
- Recognize and/or represent a geometric series, a power series, a harmonic series, a telescoping series, and a p-series.
- Determine convergence by applying the nth-term test.
- Apply the sum, difference, and product properties to determine convergence.
- Determine the convergence or divergence of a series by using the Direct Comparison Test, Limit Comparison Test, Alternating Series Test, Root Test, and Ratio Test.
- Estimate the sum of an alternating series given a maximum error value.
- Define a convergent series as absolute or conditional.
Unit 3: Essential Content and Skills
- Construct a Taylor polynomial and a Maclaurin polynomial.
- Calculate the truncation error for a geometric series.
- Determine the convergence of a Taylor series.
- Calculate the Lagrange form of the remainder for a Taylor series.
- Compute the first and second derivatives of a parametric equation.
- Establish the length of a smooth curve and curves containing vertical tangents, corners, and cusps.
- Determine the arc length of parameterized curves and cycloids.
Unit 4: Essential Content and Skills
- Discover the magnitude of a vector, the direction angle, and the component form of a vector.
- Find the velocity, acceleration, motion, and speed of vectors when given a position vector.
- Calculate the displacement and distance traveled by a particle.
- Convert between polar and rectangular coordinates.
- Identify types of polar graphs from an equation, and create polar graphs.
- Find the slope of a polar curve at a given point.
- Calculate the area inside a polar curve and between polar curves.
Course Materials
- Calculus Graphical, Numerical, Algebraic (textbook, practice book, and CD)
**NCAA approved