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Calculus: Single Variable Part 3 - Integration
  • Level Foundation
  • Duration 17 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 third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals.

Modules

About this Course

    • 2 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Learning Style Preference Survey

2 Readings

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

Indefinite Integrals

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Indefinite Integrals
  • Challenge Homework: Indefinite Integrals

1 Videos

  • Indefinite Integrals

A Simple O.D.E.

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: A Simple O.D.E.
  • Challenge Homework: A Simple O.D.E.

1 Videos

  • A Simple O.D.E.

More O.D.E.s

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: More O.D.E.s
  • Challenge Homework: More O.D.E.s

1 Videos

  • More O.D.E.s

O.D.E. Linearization

    • 2 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: O.D.E. Linearization
  • Challenge Homework: O.D.E. Linearization

2 Videos

  • O.D.E. Linearization
  • BONUS!

Integration by Substitution

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Integration by Substitution
  • Challenge Homework: Integration by Substitution

1 Videos

  • Integration by Substitution

Integration by Parts

    • 1 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Integration by Parts
  • Challenge Homework: Integration by Parts

1 Videos

  • Integration by Parts

Trig Substitution

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: Trig Substitution
  • Challenge Homework: Trig Substitution

2 Videos

  • Trig Substitution
  • BONUS!

Partial Fractions

    • 2 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Partial Fractions
  • Challenge Homework: Partial Fractions

2 Videos

  • Partial Fractions
  • BONUS!

Definite Integrals

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Core Homework: Definite Integrals

1 Videos

  • Definite Integrals

The F.T.I.C.

    • 2 Videos
    • 2 Assignment
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2 Assignment

  • Core Homework: The F.T.I.C.
  • Challenge Homework: The F.T.I.C.

2 Videos

  • The F.T.I.C.
  • BONUS!

Improper Integrals

    • 2 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Improper Integrals
  • Challenge Homework: Improper Integrals

2 Videos

  • Improper Integrals
  • BONUS!

Trigonometric Integrals

    • 1 Videos
    • 2 Assignment
Show info about module content

2 Assignment

  • Core Homework: Trigonometric Integrals
  • Challenge Homework: Trigonometric Integrals

1 Videos

  • Trigonometric Integrals

Tables and Software

    • 1 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Challenge Homework: Tables and Software

1 Videos

  • Tables and Software

Chapter 3 Review & Exam

    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Chapter 3: Integration - Exam

1 Readings

  • About the Chpater 3 Exam

Auto Summary

"Calculus: Single Variable Part 3 - Integration" is an engaging and comprehensive course offered by Coursera, focusing on the integral aspects of single-variable calculus. This course delves into key topics such as integrating differential equations, mastering various techniques of integration, understanding the fundamental theorem of integral calculus, and tackling challenging integrals. Designed for those beginning their journey in the engineering, physical, and social sciences, this course emphasizes conceptual understanding and real-world applications over mere computation. Key highlights of the course include an innovative approach to introducing and utilizing Taylor series and approximations right from the start, a unique blend of discrete and continuous calculus forms, and a unified, dynamic teaching methodology. The course spans a substantial 1020 minutes, providing learners with in-depth knowledge and skills. Subscription options are available in Starter and Professional tiers, catering to different learning needs and levels. This foundational course is perfect for students and professionals aiming to build a solid base in calculus, paving the way for advanced study and application in various scientific and engineering fields.

Robert Ghrist
Instructor

Robert Ghrist