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Calculus: Small Changes, Big Ideas

Explore the five-part curriculum. Choose a part to see its chapters and lessons.

Part I

Modeling Change

In progress

We begin by describing how quantities respond to change, then connect that idea to accumulation and differential equations. Limits arrive later to clarify and justify ideas that are already familiar.

1. Differentiation

  1. 1.1 Modeling with functions
  2. 1.2 Differentials
  3. 1.3 The derivative
  4. 1.4 Techniques of differentiation
  5. 1.5 Implicit differentiation
  6. Chapter Review

2. The shape of a curve

  1. 2.1 Increasing and decreasing behavior
  2. 2.2 Constrained optimization
  3. 2.3 Higher order derivatives
  4. 2.4 Linear approximation
  5. Chapter Review

3. Integration

  1. 3.1 The integral: accumulation of change
  2. 3.2 Properties of integrals
  3. 3.3 The Fundamental Theorem of Calculus
  4. 3.4 Average value and average rates
  5. Chapter Review

4. Differential equations

  1. 4.1 Differential equations
  2. 4.2 Exponential functions
  3. 4.3 Trigonometric functions
  4. 4.4 Logarithmic functions
  5. 4.5 Separation of variables
  6. Chapter Review

5. Limits

  1. 5.1 Limits and continuity
  2. 5.2 Algebraic techniques for limits
  3. 5.3 Limits and differentiation
  4. 5.4 Limits and integration
  5. 5.5 L’Hôpital’s Rule
  6. 5.6 Valuable theorems
  7. Chapter Review

Capstone: Numerical analysis

Card image by Moshe Harosh - Pixabay Content License