Calculus: Single Variable Part 3 - Integration
Description
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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…
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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
Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.
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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
- Reading: How Grading Works
- Reading: Your Guide to Getting Started in this Course
- Video: Indefinite Integrals
- Practice Quiz: Challenge Homework: Indefinite Integrals
- Video: A Simple O.D.E.
- Practice Quiz: Challenge Homework: A Simple O.D.E.
- Video: O.D.E.s
- Practice Quiz: Challenge Homework: O.D.E.s
- Video: O.D.E. Linearization
- Video: BONUS!
- 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
- Video: Integration by Substitution
- Practice Quiz: Challenge Homework: Integration by Substitution
- Video: Integration by Parts
- Practice Quiz: Challenge Homework: Integration by Parts
- Video: Trig Substitution
- Video: BONUS!
- Practice Quiz: Challenge Homework: Trig Substitution
- Video: Partial Fractions
- Video: BONUS!
- 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
- Video: Definite Integrals
- Video: The F.T.I.C.
- Video: BONUS!
- 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
- Video: Improper Integrals
- Video: BONUS!
- Practice Quiz: Challenge Homework: Improper Integrals
- Video: Trigonometric Integrals
- Practice Quiz: Challenge Homework: Trigonometric Integrals
- Video: Tables and Software
- Practice Quiz: Challenge Homework: Tables and Software
- Reading: About the Chpater 3 Exam
Graded: Core Homework: Improper Integrals
Graded: Core Homework: Trigonometric Integrals
Graded: Chapter 3: Integration - Exam
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