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Single Variable Calculus
  • Level Foundation
  • Duration 14 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 fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam.

Modules

About the Course

    • 2 Readings
Show info about module content

2 Readings

  • Your Guide to Getting Started in this Course
  • How Grading Works

Sequences

    • 2 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Sequences

2 Videos

  • Sequences
  • BONUS!

Differences

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Differences
  • Challenge Homework: Differences

1 Videos

  • Differences

Discrete Calculus

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Discrete Calculus
  • Challenge Homework: Discrete Calculus

1 Videos

  • Discrete Calculus

Numerical O.D.E.s

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Numerical O.D.E.s

1 Videos

  • Numerical O.D.E.s

Numerical Integration

    • 1 Videos
Show info about module content

1 Videos

  • Numerical Integration

Infinite Series

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Infinite Series
  • Challenge Homework: Infinite Series

1 Videos

  • Infinite Series

Convergence Tests I

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Convergence Tests I
  • Challenge Homework: Convergence Tests I

1 Videos

  • Convergence Tests I

Convergence Tests II

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Convergence Tests II

1 Videos

  • Convergence Tests II

Absolute & Conditional

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Absolute & Conditional

1 Videos

  • Absolute & Conditional

Power Series

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Power Series
  • Challenge Homework: Power Series

1 Videos

  • Power Series

Taylor Series Redux

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Taylor Series Redux
  • Challenge Homework: Taylor Series Redux

1 Videos

  • Taylor Series Redux

Approximation and Error

    • 2 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Approximation and Error

2 Videos

  • Approximation and Error
  • BONUS!

Calculus Redux

    • 2 Videos
Show info about module content

2 Videos

  • Calculus Redux
  • BONUS!

Foreshadowing

    • 1 Videos
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1 Videos

  • Foreshadowing

Credits

    • 1 Videos
Show info about module content

1 Videos

  • Credits

Chapter 5 Review & Exam

    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Chapter 5: Discretization - Exam

1 Readings

  • About the Chapter 5 Exam

THE 5-CHAPTER GREAT BIG FINAL EXAM

    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • 5-CHAPTER GREAT BIG FINAL EXAM!

1 Readings

  • About the 5-CHAPTER GREAT BIG FINAL EXAM!

Auto Summary

Unlock the fascinating world of mathematical analysis with the "Single Variable Calculus" course, designed to illuminate the fundamental principles of calculus and their real-world applications. This comprehensive course is perfect for budding engineers, physical scientists, and social scientists who are beginning their academic journeys. Embark on an enlightening educational experience led by expert instructors from Coursera, where you'll delve into essential topics such as sequences, numerical methods, series and convergence tests, and power and Taylor series. This course stands out by integrating Taylor series and approximations from the start, blending discrete and continuous calculus, and prioritizing conceptual understanding over mere computational skills. Spanning 840 minutes of engaging content, this course offers a clear, dynamic, and unified approach to learning, culminating in a final exam that allows you to earn a verified certificate upon successful completion. Join the Starter subscription to begin your foundational journey in single-variable calculus and equip yourself with the knowledge to excel in various scientific fields.

Robert Ghrist
Instructor

Robert Ghrist