Advanced Math · Level 2
2.1 Calculus Fundamentals
Begin your calculus journey by getting up to speed on limits and derivatives.
Indeterminate Forms
Limits Intuition
Limits of Functions
Infinite Limits
Continuity
Computing Limits I
Computing Limits II
The Squeeze Theorem
IVT Application: Root Finder
Precise Definition of Limits
The Derivative at a Point
First Examples of Derivatives
What Derivatives Tell Us
The Second Derivative
Real-World Derivatives
Average vs. Instantaneous
Polynomials
Products, Reciprocals, and Quotients
Trigonometric Functions
The Chain Rule
Exponentials and Logarithms
Linear Approximation
Pendulums: An Application
Optimization
Implicit Differentiation
L'Hôpital's Rule
Antiderivatives & Integrals
Course description
Calculus is the mathematical study of things that change: cars accelerating, planets moving around the sun, economies fluctuating. To study these changing quantities, a new set of tools - calculus - was developed in the 17th century, forever altering the course of math and science. This course sets you on the path to calculus fluency. The first part provides a firm intuitive understanding of limits, the central idea underlying the entire subject. The second part applies limits to define derivatives, an indispensable tool for measuring change. By the end of the course you'll have practical calculus experience that any aspiring scientist, engineer, or mathematician needs.
Topics covered
- Continuity
- Derivatives
- Extrema
- Implicit Derivatives
- L'Hôpital's Rule
- Limits
- Newton's Method
- Physics Applications
- The Chain Rule
- The Squeeze Theorem
Prerequisites and next steps
You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts. You should also be familiar with exponential functions, logarithms, and basic trigonometric identities.
Prerequisites
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Advanced Math · Level 2
2.2 Integral Calculus
Take the next step on the calculus journey with integrals and sums.
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