Advanced Calculus A / B

Calculus is the mathematics of change.  It is used to solve complex problems that are continuously evolving and would otherwise be unsolvable with only algebra and geometry.  This online advanced placement course is designed to prepare students to become deep mathematical thinkers.  You will explore the calculus concepts of limits, differentiation, and integration and apply those concepts in meaningful ways.  The course is split into two semesters.  The first semester focuses on the concepts of functions, limits, and differentiation and their applications.  The second semester builds off the first semester to focus on integrations.  It will cover topics such as the definite and indefinite integral and their applications, inverse function, and techniques for integrating. Course Goals By the end of the course the student will be able to:

• Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal, and understand the connections among these representations.
• Understand the meaning of the derivative in terms of a rate of change and local linear approximation and 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 change and 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 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.