AP Calculus BC

CALCULUS BC SYLLABUS

Mr. P. Nelson

pnelson0502@yahoo.com

Course Description

AP Calculus BC is primarily concerned with developing the students' understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Broad concepts and widely applicable methods are emphasized. Technology is used regularly by students to reinforce relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. Through the use of the unifying themes of derivatives, integrals, limits, approximations, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. AP Calculus BC students study the topics covered in college-level Calculus I and Calculus II.

Semester 1

• Functions and graphs

• Limits and continuity

• Concept of the derivative

• Local linearity and differentiability

• Computation of derivatives

• Applications of derivatives

• Antiderivatives

• Riemann sums

• Fundamental Theorem of Calculus

• Functions defined by integrals

• Techniques of antidifferentiation

• Numerical approximations

• Differential equations

• Slope fields and Euler's method

• Area and volume

• Definite integral as an accumulator

Semester 2

• Integration techniques

• Logistic growth

• Parametric functions

• Vectors

• Polar functions

• Convergence and divergence of a series of constants

• Taylor polynomials and power series

• Review for AP test

• Hyperbolic functions

• More on differential equations

CalcChat: https://www.calcchat.com/book/Calculus-8e/

Materials Needed:

• Calculus (8th Edition) by Larson, Hostetler, and Edwards

• Notebook paper

• #2 pencils

• TI-83, TI-84, TI-89, or TI-Nspire graphing calculator

Evaluation:

Grades will be determined by major grades and daily grades. Major grades include tests and quizzes. Daily grades may include homework and classwork. Homework is checked daily, and each count as a daily grade. The major grade average will count as 70% of each student's grade while the daily average grade will count as 30% of the student's grade.

Link to the College Board's AP Calculus BC Website:

https://apcentral.collegeboard.org/courses/ap-calculus-bc/course?course=ap-calculus-bc