AP Calculus - INDIF Technologies Inc

Limits are the backbone of Calculus. They are what allow Derivatives and Integrals to work. We will explore all the limits-based topics covered on the AP Calculus Exam including L’Hopital’s Rule, Estimating Limits, Limit Operations, Infinite Limits, and More! Further, we will explore Continuity and look at how we can better analyze functions to obtain meaningful and useful results when taking Derivatives or Integrals!

📉 Differentiation

Learn how to perform derivatives using the Limit Definition of the Derivative, Power Rule, Chain Rule, Product Rule, Quotient Rule, and more! With our plethora of videos, worksheets, practice problems, practice exams, and other resources, you will be prepared to take derivatives of any function including high-order functions as well!

📈 Application of Differentiation

Learn how to use the concepts of Derivatives in the real-world in fields that transcend beyond Mathematics such as Physics, Biology, Engineering, etc. Through concepts like Related Rates and Optimization, we will explore how we can use derivatives to better explain the mathematical relationships in our world, and see how engineers develop revolutionary solutions.

📏 Integration

Learn how to perform Integrals using the Reverse Power Rule, Reverse Chain Rule, and other related rules. Learn about key calculus concepts like the Fundamental Theorem of Calculus I and II, and explore how we can estimate areas under curves using Riemann Approximations.

📊 Application of Integration

Learn how to use the concepts of Integrals in the real-world in fields that transcend beyond Mathematics such as Physics, Biology, Engineering, etc. Through concepts like Area and Volume of Integration, we will explore how we can use Integrals to better explain the mathematical relationships in our world, and see how engineers develop revolutionary solutions.

🔣 Differential Equations

Differential Equations are extremely important in the context of STEM fields like Engineering and Biology. They allow us to analyze the mathematical proportions and rates present in our world. Differential Equations make use of both Derivatives and Integrals and are very useful for exploring the world that we live in.

🌀 Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC)

Parametric Equations and Polar Coordinates are great ways to analyze a new way of thinking: The Polar Plane. Throughout our life, we have been exposed to Cartesian or Rectangular equations, coordinates, and the coordinate plane. Therefore, some may find it difficult to analyze Polar Curves, however, we have clarified its topic to make is as easily digestible as possible.

➕ Infinite Sequences and Series (BC)

Infinite Series and Sequences presents another application of Derivative and Integrals. In fact, Integrals can be expressed as just Infinite Series of the area of a particular cross section (generally a rectangle) under a curve. With concepts such as Maclaurin/Taylor Series, and Alternating Series, we can analyze Infinite Series sucessfully on the AP Calculus Exam.