Investigate the central ideas of calculus and learn how to put them to use.
Rate of Change
Rate of Change: Practice Questions
Rate of Change: Challenge Questions
Instantaneous Rate of Change
Instantaneous Rate of Change: Practice Questions
Instantaneous Rate of Change: Challenge Questions
The Derivative: Practice Questions
The Derivative: Challenge Questions
Applying the Derivative: Optimization
Optimization: Practice Questions
Optimization: Challenge Questions
What is a Derivative?
What are Derivatives for?
How are Derivatives found?
What is an Integral?
How are Integrals found?
Application: Gabriel's Horn
What is an Infinite Sum?
The Tower of Lire
What are Infinite Sums for?
Sine & Cosine
Calculus has such a wide scope and depth of application that it's easy to lose sight of the forest for the trees. This course takes a bird's-eye view, using visual and physical intuition to present the major pillars of calculus: limits, derivatives, integrals, and infinite sums. You'll walk away with a clear sense of what calculus is and what it can do. Calculus in a Nutshell is a short course with only 19 quizzes. If you want to quickly learn an overview of calculus or review the foundational principles after a long hiatus from the subject, this course ought to be perfect. Calculus Fundamentals and Integral Calculus are the two courses that can follow next in the Calculus sequence. If/when you want to go into more depth and learn a wide spread of specific techniques in differential calculus and integral calculus respectively, that's where you should look. For example, integration techniques like "integration by parts" are only in the Integral Calculus course.
- Derivative rules
- The Fundamental Theorem
- Geometric applications
- Geometric series
- Infinite sums
- Riemann sums
- Science applications
- Tangent lines
Prerequisites and next steps
You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts.