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Calculus: Single Variable Part 4 - Applications
  • Level Foundation
  • Duration 21 hours
  • Course by University of Pennsylvania
  • Offered by

About

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.

Modules

About the Course

    • 2 Readings
    • 1 Assignment
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1 Assignment

  • Learning Style Preference Survey

2 Readings

  • How to Get Started in this Course
  • How Grading Works

Simple Areas

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Simple Areas
  • Challenge Homework: Simple Areas

1 Videos

  • Simple Areas

Complex Areas

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Complex Areas
  • Challenge Homework: Complex Areas

2 Videos

  • Complex Areas
  • BONUS!

Volumes

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Simple Volumes
  • Challenge Homework: Simple Volumes

2 Videos

  • Volumes
  • BONUS!

Complex Volumes

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Complex Volumes
  • Challenge Homework: Complex Volumes

1 Videos

  • Complex Volumes

Volume & Dimension

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Volume and Dimension
  • Challenge Homework: Volume and Dimension

2 Videos

  • Volume & Dimension
  • BONUS

Arclength

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Arclength
  • Challenge Homework: Arclength

1 Videos

  • Arclength

Surface Area

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Surface Area
  • Challenge Homework: Surface Area

1 Videos

  • Surface Area

Work

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Work
  • Challenge Homework: Work

1 Videos

  • Work

Elements

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Elements
  • Challenge Homework: Elements

2 Videos

  • Elements
  • BONUS!

Averages

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Averages
  • Challenge Homework: Averages

1 Videos

  • Averages

Centroids

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Centroids
  • Challenge Homework: Centroids

2 Videos

  • Centroids
  • BONUS!

Moments and Gyrations

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Moments and Gyrations
  • Challenge Homework: Moments and Gyrations

2 Videos

  • Moments and Gyrations
  • BONUS!

Fair Probability

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Fair Probability
  • Challenge Homework: Fair Probability

1 Videos

  • Fair Probability

Probability Densities

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Probability Densities
  • Challenge Homework: Probability Densities

1 Videos

  • Probability Densities

Expectation and Variance

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Expectation and Variance
  • Challenge Homework: Expectation and Variance

1 Videos

  • Expectation and Variance

Chapter 4 Review & Exam

    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Chapter 4: Applications - Exam

1 Readings

  • About the Chapter 4 Exam

Auto Summary

Explore the fascinating world of single-variable Calculus with a focus on applications in this engaging course by Coursera. Ideal for beginners in engineering, physical, and social sciences, this foundation-level course emphasizes conceptual understanding over computation. Topics include geometric and physical applications, areas, volumes, averages, mass, and an introduction to probability. Enjoy a clear and dynamic learning experience over 1260 minutes with the Starter subscription. Perfect for those eager to grasp the profound achievements of human thought in Calculus.

Robert Ghrist
Instructor

Robert Ghrist