Calculus

From Teach And Discover Wiki

Welcome to the Calculus course page. Below you will find a course outline with the text and other information you will need in order to complete the course. This is a one-year course covering differential calculus (first semester) and integral calculus (second semester). The course is designed to prepare it's students to pass the AP Calculus exam and earn college credit. The course is recommended for those who will pursue careers in science, mathematics, and/or engineering.

Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series, and constitutes a major part of modern university education. Historically, it was sometimes referred to as "the calculus of infinitesimals", but that usage is seldom seen today.

Calculus has widespread applications in science and engineering and is used to solve complicated problems for which algebra alone is insufficient. Calculus builds on algebra, Trigonometry, and analytic geometry and includes two major branches, differential calculus and integral calculus, that are related by the fundamental theorem of calculus. In more advanced mathematics, calculus is usually called Real Analysis and is defined as the study of functions.

More generally, calculus can refer to any method or system of calculation.

Contents 1 Course Outline 2 AP Calculus AB 2.1 Purpose 2.2 Course Content

Course Outline

AP Calculus AB

AP Calculus AB is an advanced placement calculus course taken by high school students around the world, most of whom study at schools with an American curriculum. The course is traditionally taken after Precalculus, otherwise known as Introduction to Analysis, and is the first calculus course offered at most schools.

Purpose

"Calculus AB can be offered by an AP course by any school that can organize a curriculum for students with mathematical ability... Students who take an AP Calculus course should do so with the intention of placing out of a comparable college calculus course."

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Course Content

The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus. More specifically, the topics are

• Analysis of graphs (predicting and explaining behavior)
• Limits of functions (one and two sided)
• Asymptotic and unbounded behavior
• Continuity
• Derivatives
  • Concept
  • At a point
  • As a function
  • Applications
  • Second derivatives
• Integrals
  • Interpretations
  • Properties
  • Applications
  • Techniques
  • Numerical approximations
• Fundamental theorem of calculus
• Antidifferentation