AP Calculus
Course Overview
AP Calculus is an important branch of calculus, which is a course for college students. It is a tool for students to study day-to-day problems analytically through graphical and numerical methods.
In this, various types of mathematical problems are solved using theorems. Integration, differentiation, and limits are studied in this course.
The syllabus of AP Calculus contains the following topics:
Unit 1: Limits and Continuity
You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.
Unit 2: Differentiation: Definition and Fundamental Properties
You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
Unit 5: Analytical Applications of Differentiation
After exploring relationships among the graphs of a function and its derivatives, you’ll learn to apply calculus to solve optimization problems.
Unit 6: Integration and Accumulation of Change
You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques.
Unit 7: Differential Equations
You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay.
Unit 8: Applications of Integration
You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.