Big Picture of Calculus

This module explores the overarching themes of calculus, emphasizing its focus on change. Professor Strang illustrates the concept of calculus through relatable examples from everyday life, including:

• Driving a car and understanding speed.
• Climbing a mountain and the effort involved.
• Growing to full adult height and the rates of growth.

By connecting calculus to familiar scenarios, students can better grasp its significance and application in the world around them.

Course Lectures

• Professor Strang Introduces the Series

  Gilbert Strang

  Play

  In this introductory module, Professor Gilbert Strang shares his motivation for creating the Highlights of Calculus series. He explains how the materials benefit MIT OpenCourseWare users and the general audience. This informal discussion takes place in his office at MIT, providing insights into the importance of calculus and its foundational ideas.

  By setting the stage for the series, attendees are encouraged to appreciate the beauty and utility of calculus in various fields.

• Big Picture of Calculus

  Gilbert Strang

  Playing

  This module explores the overarching themes of calculus, emphasizing its focus on change. Professor Strang illustrates the concept of calculus through relatable examples from everyday life, including:

  • Driving a car and understanding speed.
  • Climbing a mountain and the effort involved.
  • Growing to full adult height and the rates of growth.

  By connecting calculus to familiar scenarios, students can better grasp its significance and application in the world around them.

• Big Picture: Derivatives

  Gilbert Strang

  Play

  This module delves into the concept of derivatives in calculus. Professor Strang explains how calculus enables us to find the relationship between distance and speed. He discusses:

  • The simplicity of constant speed versus the complexity of changing speed.
  • How to determine the rate of change of a function.
  • The significance of the slope of a curve.

  Through visual aids and examples, students will develop a clearer understanding of derivatives and their practical relevance.

• Max and Min and Second Derivatives

  Gilbert Strang

  Play

  In this module, Professor Strang examines critical points in calculus, focusing on maxima and minima. He explains that:

  • At the top and bottom of a curve, the slope is zero.
  • The second derivative helps determine whether the curve bends up or down.

  Using a real-world scenario, he discusses how to find the most efficient route from home to work, demonstrating the application of calculus in decision-making.

• The Exponential Function

  Gilbert Strang

  Play

  In this module, Professor Strang introduces the exponential function and its remarkable properties. He explains:

  • The significance of the number e and its connection to everyday concepts like bank interest.
  • How the graph of y = e^x possesses the unique feature that its slope equals its height.
  • The implications of rapid growth described by exponential functions.

  This exploration lays the groundwork for understanding more complex calculus topics and showcases the beauty of mathematical functions.

• Big Picture: Integrals

  Gilbert Strang

  Play

  This module covers the second half of calculus, focusing on integrals and their role in understanding distance traveled over time. Professor Strang explains:

  • How integrals are essentially the opposite of derivatives.
  • The process of adding up small pieces to calculate total distance.
  • Real-life applications of integrals in various scenarios.

  By the end of this module, students will have a solid grasp of integrals and their significance in the broader context of calculus.