Calculus: Single Variable Part 3 - Integration

Product type

Calculus: Single Variable Part 3 - Integration

Coursera (CC)
Logo Coursera (CC)
Provider rating: starstarstarstar_halfstar_border 7.2 Coursera (CC) has an average rating of 7.2 (out of 6 reviews)

Need more information? Get more details on the site of the provider.

Description

When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: 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, un…

Read the complete description

Frequently asked questions

There are no frequently asked questions yet. If you have any more questions or need help, contact our customer service.

Didn't find what you were looking for? See also: .

When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: 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.

Created by:  University of Pennsylvania
  • Taught by:  Robert Ghrist, Professor

    Mathematics and Electrical & Systems Engineering
Commitment 6-8 hours/week Language English, Subtitles: Spanish How To Pass Pass all graded assignments to complete the course. Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

Help from your peers

Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.

University of Pennsylvania The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.

Syllabus


WEEK 1


Integrating Differential Equations



Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.


5 videos, 2 readings, 4 practice quizzes expand


  1. Reading: How Grading Works
  2. Reading: Your Guide to Getting Started in this Course
  3. Video: Indefinite Integrals
  4. Practice Quiz: Challenge Homework: Indefinite Integrals
  5. Video: A Simple O.D.E.
  6. Practice Quiz: Challenge Homework: A Simple O.D.E.
  7. Video: O.D.E.s
  8. Practice Quiz: Challenge Homework: O.D.E.s
  9. Video: O.D.E. Linearization
  10. Video: BONUS!
  11. Practice Quiz: Challenge Homework: O.D.E. Linearization

Graded: Core Homework: Indefinite Integrals
Graded: Core Homework: A Simple O.D.E.
Graded: Core Homework: O.D.E.s
Graded: Core Homework: O.D.E. Linearization

WEEK 2


Techniques of Integration
Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.


6 videos, 4 practice quizzes expand


  1. Video: Integration by Substitution
  2. Practice Quiz: Challenge Homework: Integration by Substitution
  3. Video: Integration by Parts
  4. Practice Quiz: Challenge Homework: Integration by Parts
  5. Video: Trig Substitution
  6. Video: BONUS!
  7. Practice Quiz: Challenge Homework: Trig Substitution
  8. Video: Partial Fractions
  9. Video: BONUS!
  10. Practice Quiz: Challenge Homework: Partial Fractions

Graded: Core Homework: Integration by Substitution
Graded: Core Homework: Integration by Parts
Graded: Core Homework: Trig Substitution
Graded: Core Homework: Partial Fractions

WEEK 3


The Fundamental Theorem of Integral Calculus



Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.


3 videos, 1 practice quiz expand


  1. Video: Definite Integrals
  2. Video: The F.T.I.C.
  3. Video: BONUS!
  4. Practice Quiz: Challenge Homework: The F.T.I.C.

Graded: Core Homework: Definite Integrals
Graded: Core Homework: The F.T.I.C.

WEEK 4


Dealing with Difficult Integrals



The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.


4 videos, 1 reading, 3 practice quizzes expand


  1. Video: Improper Integrals
  2. Video: BONUS!
  3. Practice Quiz: Challenge Homework: Improper Integrals
  4. Video: Trigonometric Integrals
  5. Practice Quiz: Challenge Homework: Trigonometric Integrals
  6. Video: Tables and Software
  7. Practice Quiz: Challenge Homework: Tables and Software
  8. Reading: About the Chpater 3 Exam

Graded: Core Homework: Improper Integrals
Graded: Core Homework: Trigonometric Integrals
Graded: Chapter 3: Integration - Exam
There are no reviews yet.

    Share your review

    Do you have experience with this course? Submit your review and help other people make the right choice. As a thank you for your effort we will donate $1.- to Stichting Edukans.

    There are no frequently asked questions yet. If you have any more questions or need help, contact our customer service.