Interactive worksheets for Calculus I


Modules

An introduction to SAGE
  1. Limits
    1. Limits: intuitive definition
    2. Limits: precise definition
    3. Limits: properties
    4. The Squeeze Theorem
    5. Continuity
    6. Applications of the Intermediate Value Theorem
    7. Limits at ∞
    8. Asymptotes
    9. Problems with limits at ∞
    10. Extensions of continuous functions
  2. Derivatives, with elementary applications
    1. Derivatives: intuitive definition
    2. Derivatives: precise definition
    3. Finding derivatives by experimentation
    4. Properties of derivatives
    5. Derivatives of polynomials
    6. Linear approximations
    7. Derivatives of trigonometric functions
    8. Newton's Method
    9. The Chain Rule
    10. Derivatives of exponential functions
    11. Implicit differentiation
    12. Derivatives of logarithmic functions
  3. Advanced applications of derivatives
    1. Related rates
    2. The Mean Value Theorem
    3. Extrema
    4. Optimization
    5. Issues in optimization
    6. Curve sketching
    7. L'Hôpital's Rule
    8. The growth of derivatives

Useful links

SAGElets (interactive SAGE applications)

(Preview snapshots that open in new window)

Labs

  • Experimental limits: Lab (PDF)
  • Squeezing the floor: Worksheet
    (after completing the Squeeze Theorem module)
  • Tangent lines on a cubic: Worksheet
    Preview: PNG, JPG
    (after completing derivatives)
  • The cherry and the glass: Worksheet
    Preview: PNG, JPG
    (after completing derivatives of polynomials)
  • Connecting two highways: Lab, Worksheet
    Preview: PNG, JPG
    (after completing derivatives of polynomials)
  • Waves and trigonometric polynomials: Worksheet
    Preview: PNG, JPG
    (after completing derivatives of trigonometric functions)
  • From linear to non-linear approximations: Worksheet
    Preview: PNG, JPG
    (after completing linear approximations)
  • The derivative of an inverse function: Worksheet
    Preview: PNG, JPG
    (after completing implicit differentiation)