Calculus
28 interactive notebooks ready to launch.
// Unit 0: Pre-calculus
// Unit 1: Derivatives
The Difference Quotient
Visualizing the foundational definition of a derivative using secant slope limits.
Derivative Applications
Using derivatives to optimize functions and solve real-world rate problems.
Building the Engine
Constructing the core machinery of differential calculus from first principles.
Teaching the Engine: Calculus
Exploring how the calculus engine generalizes and applies to broader mathematical problems.
Root Finding
Using numerical methods and derivatives to locate the roots of functions.
Optimization
Finding maxima and minima of functions using derivative-based techniques.
Curve Sketching
Analyzing derivatives to understand the shape and behavior of functions.
Kinematics
Applying derivatives to model motion, velocity, and acceleration.
// Unit 2: Integration
Numerical Integration
Approximating definite integrals using computational numerical methods.
Convergence and Accumulation
Understanding accumulation, convergence, and the intuition behind integration.
Fundamental Theorem of Calculus
Connecting differentiation and integration through the Fundamental Theorem of Calculus.
Symbolic Integration
Computing antiderivatives analytically and with symbolic mathematics tools.
Area Between Curves
Applying integration to compute the area enclosed by multiple functions.
Kinematics Part 2
Using integration to analyze displacement, velocity, and acceleration.
Statistics and Probability
Exploring how integration underpins probability distributions and statistical concepts.
// Unit 3: Differential Equations Introduction
// Unit 4: Multivariable Calculus
Multivariable Functions and Plotting
Visualizing functions of several variables using computational tools.
Numerical Partial Derivatives
Approximating partial derivatives and interpreting multivariable rates of change.
3D Optimization
Finding extrema of multivariable functions using gradients and critical points.
Double Integrals
Computing double integrals over regions in two dimensions.
The Hessian Matrix
Using the Hessian matrix to classify critical points of multivariable functions.
// Unit 5: Vector Calculus
Vector Fields
Representing and visualizing vector fields in two and three dimensions.
Line Integrals
Computing work and circulation using line integrals through vector fields.
Divergence and Curl
Exploring the local behavior of vector fields through divergence and curl.
The Grand Theorems
Connecting line, surface, and volume integrals through the major theorems of vector calculus.
Maxwell Equations
Applying vector calculus to understand Maxwell's equations and classical electromagnetism.