Mr. Integral

Understand change

Calculus I

Follow one idea from limits to derivatives and integrals. See how slopes and areas fit together.

Start learning 4 units · 27 lessons

The course, unit by unit.

Open a unit for its introduction, map and lesson route.

01Optional Function RefresherReview notation and graph behavior before beginning limits.5 lessons

Which graph-reading skills do limits rely on?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Domain and Range
  2. 02Graphing Piecewise Functions
  3. 03Shifting a Graph
  4. 04The Signum Function
  5. 05The Greatest Integer Function
02Limits & ContinuityWhat a function approaches - even where it is not defined.5 lessons

What happens as we get close to a point?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Limits and One-Sided Behavior
  2. 02Continuity and Piecewise Functions
  3. 03Intermediate Values and Root Bracketing
  4. 04Infinite Limits and Asymptotes
  5. 05Factoring, Rationalizing and Squeezing Limits
03The DerivativeThe slope machine: rates of change and what they reveal about a graph.12 lessons

How can we measure change at a single instant?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference

Definition and differentiation methods

  1. 01The Derivative from First Principles
  2. 02Power Rules and Linearity
  3. 03Product and Quotient Rules
  4. 04The Chain Rule
  5. 05Exponential, Logarithmic and Trigonometric Derivatives
  6. 06Implicit and Logarithmic Differentiation

Theorems and graph behavior

  1. 07Rolle’s Theorem and the Mean Value Theorem
  2. 08Reading Graphs with Derivatives

Models and approximation

  1. 09Optimization from a Model
  2. 10Related Rates and Units
  3. 11Linear Approximation and Newton’s Method
  4. 12Indeterminate Forms and L’Hôpital’s Rule
04The IntegralAccumulate change: areas, Riemann sums, and the inverse of the derivative.5 lessons

How do tiny changes add up to a total?

Start with the introduction & map →
Unit cheat sheet All the key ideas in one reference
  1. 01Antiderivatives and Initial Values
  2. 02Riemann Sums and Accumulation
  3. 03Definite Integrals and the Fundamental Theorem
  4. 04Substitution and Transformed Bounds
  5. 05Net Change, Distance and a Calculus I Checkpoint