AP Calculus AB
Electronic copy of 1st Day of School Packet: Click HERE to download a copy of the Welcome Letter, Supply List and Course Syllabus.
***Non-secure class documents can be found on the documents page. Secure class documents (Lesson handouts, Power Point presentations, solutions, etc) can be found on Google Classroom***
Text:
Finney, Demana, Waits, and Kennedy. Calculus: Graphical, Numerical, Algebraic,4th ed. New Jersey: Prentice Hall, 2011.
Briggs, Cochran, and Gillet. Calculus: Early Transcendentals, 2nd ed. Boston: Pearson, 2015
Course Objectives: Students should be able to:
to satisfactorily pass the AP EXAM.
work with functions represented in a variety of ways: graphically, numerically, analytically, or verbally. They should understand the connections among these representations.
understand the meaning of the derivative in terms of a rate of change and local linear approximation.
use derivatives to solve a variety of problems.
understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change.
use integrals to solve a variety of problems.
understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.
model a written description of a physical situation with a function, a differential equation, or an integral.
use technology to help solve problems, experiment, interpret results, and verify conclusions.
determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
Topics Covered:
Functions, Graphs, and Limits
Analysis of Graphs
Limits of Functions (including one-sided limits)
Asymptotic and unbounded behavior
Continuity as a property of functions
Derivatives
Concept of a derivative
Derivative at a point
Derivative of a function
Second Derivatives
Application of Derivatives
Computation of Derivatives
Integrals
Interpretations and properties of definite integrals
Application of integrals
Fundamental Theorem of Calculus
Techniques of antidifferentiation
Application of antidifferentiation
Numerical approximation to definite integrals