Overview

Conquer calculus—one of the most powerful and useful of all mathematical skills—with this simple and brilliant guide taught by award-winning mathematician Michael Starbird. This course consists of 24 lessons designed to make calculus accessible to everyone, even those with only a basic understanding of algebra and geometry. You will learn about the two core concepts of calculus: derivatives and integrals, which give insight into motion and change.

Course Instructor

Michael Starbird, an award-winning professor of mathematics at the University of Texas at Austin, takes you on an engaging journey through the world of calculus, making complex concepts approachable and enlightening.

Video Lessons

• Two Ideas, Vast Implications
  • Duration: 33 min
  • Description: Explore the importance of calculus and its two fundamental ideas related to motion and change.

2. Stop Sign Crime-The First Idea of Calculus-The Derivative
   • Duration: 31 min
   • Description: Learn about derivatives through real-life scenarios, like a car approaching a stop sign.

• Another Car, Another Crime-The Second Idea of Calculus-The Integral
  • Duration: 31 min
  • Description: Understand integrals through the concept of calculating position based on speed.

• The Fundamental Theorem of Calculus
  • Duration: 31 min
  • Description: Discover the relationship between derivatives and integrals through a moving car example.

5. Visualizing the Derivative-Slopes
   • Duration: 31 min
   • Description: Learn how graphs can visualize the derivative’s role in quantifying change.

• Derivatives the Easy Way-Symbol Pushing
  • Duration: 31 min
  • Description: Explore how derivatives can show the relationship between changing variables.

• Abstracting the Derivative-Circles and Belts
  • Duration: 32 min
  • Description: Learn to find derivatives algebraically to simplify complex calculus processes.

• Circles, Pyramids, Cones, and Spheres
  • Duration: 31 min
  • Description: Examine projectile motion and speed using calculus concepts.

• Archimedes and the Tractrix
  • Duration: 31 min
  • Description: Understand optimization problems and their importance using calculus strategies.

10. The Integral and the Fundamental Theorem
    • Duration: 29 min
    • Description: Learn how ancient methods inform modern integral calculus.

11. Abstracting the Integral-Pyramids and Dams
    • Duration: 30 min
    • Description: Discover how slicing shapes can lead to the computation of areas and volumes through integrals.

12. Buffon’s Needle or ? from Breadsticks
    • Duration: 32 min
    • Description: Understand the concept of the integral as a sum of small changes.

13. Achilles, Tortoises, Limits, and Continuity
    • Duration: 31 min
    • Description: Solve problems related to volume and pressure using the integral strategy.

14. Calculators and Approximations
    • Duration: 32 min
    • Description: Connect the derivative and integral through the Fundamental Theorem’s shortcuts.

• The Best of All Possible Worlds-Optimization
  • Duration: 31 min
  • Description: Explore how calculus can solve probability problems, such as Buffon’s needle experiment.

16. Economics and Architecture
    • Duration: 30 min
    • Description: Investigate Zeno’s Arrow Paradox and how continuity solves seemingly paradoxical problems.

• Galileo, Newton, and Baseball
  • Duration: 31 min
  • Description: Understand the continuum of real numbers and their application in models.

18. Getting off the Line-Motion in Space
    • Duration: 30 min
    • Description: Learn how infinite series can provide exact approximations for irrational numbers.

19. Mountain Slopes and Tangent Planes
    • Duration: 31 min
    • Description: Extend calculus concepts to analyze situations involving multiple variables.

20. Several Variables-Volumes Galore
    • Duration: 31 min
    • Description: Apply calculus to various objects moving in three-dimensional space.

21. The Fundamental Theorem Extended
    • Duration: 31 min
    • Description: Explore how calculus describes diverse physical phenomena across multiple fields.

• Fields of Arrows-Differential Equations
  • Duration: 32 min
  • Description: Use calculus to analyze rates of change in economic models.

• Owls, Rats, Waves, and Guitars
  • Duration: 32 min
  • Description: Examine population models and the applicability of calculus in predicting trends.

24. Calculus Everywhere
    • Duration: 32 min
    • Description: Understand the indispensable role of calculus in explaining various aspects of life.