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Englisch

Untertitel: Englisch, Spanisch

Kompetenzen, die Sie erwerben

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution

100 % online

Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.

Flexible Fristen

Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.

Ca. 22 Stunden zum Abschließen

Empfohlen: 6-8 hours/week...

Englisch

Untertitel: Englisch, Spanisch

Lehrplan - Was Sie in diesem Kurs lernen werden

Woche
1
3 Stunden zum Abschließen

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.

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5 Videos (Gesamt 75 min), 2 Lektüren, 8 Quiz
5 Videos
A Simple O.D.E.16m
More O.D.E.s15m
O.D.E. Linearization16m
BONUS!8m
2 Lektüren
How Grading Works10m
Your Guide to Getting Started in this Course10m
8 praktische Übungen
Core Homework: Indefinite Integrals10m
Challenge Homework: Indefinite Integrals2m
Core Homework: A Simple O.D.E.10m
Challenge Homework: A Simple O.D.E.4m
Core Homework: More O.D.E.s10m
Challenge Homework: More O.D.E.s8m
Core Homework: O.D.E. Linearization14m
Challenge Homework: O.D.E. Linearization6m
Woche
2
2 Stunden zum Abschließen

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.

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6 Videos (Gesamt 76 min), 8 Quiz
6 Videos
Integration by Parts16m
Trig Substitution15m
BONUS!7m
Partial Fractions15m
BONUS!6m
8 praktische Übungen
Core Homework: Integration by Substitution12m
Challenge Homework: Integration by Substitution4m
Core Homework: Integration by Parts14m
Challenge Homework: Integration by Parts6m
Core Homework: Trig Substitution12m
Challenge Homework: Trig Substitution6m
Core Homework: Partial Fractions12m
Challenge Homework: Partial Fractions6m
Woche
3
1 Stunde zum Abschließen

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.

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3 Videos (Gesamt 46 min), 3 Quiz
3 Videos
The F.T.I.C.16m
BONUS!12m
3 praktische Übungen
Core Homework: Definite Integrals10m
Core Homework: The F.T.I.C.10m
Challenge Homework: The F.T.I.C.8m
Woche
4
2 Stunden zum Abschließen

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.

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4 Videos (Gesamt 50 min), 1 Lektüre, 6 Quiz
4 Videos
BONUS!6m
Trigonometric Integrals15m
Tables and Software11m
1 Lektüre
About the Chpater 3 Exam10m
6 praktische Übungen
Core Homework: Improper Integrals16m
Challenge Homework: Improper Integrals10m
Core Homework: Trigonometric Integrals12m
Challenge Homework: Trigonometric Integrals4m
Challenge Homework: Tables and Software8m
Chapter 3: Integration - Exam20m
4.9
31 BewertungenChevron Right

Top reviews from Calculus: Single Variable Part 3 - Integration

von CCJul 2nd 2018

I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.

von ABJun 18th 2016

A bit difficult, but not truly when a good effort is made. No doubt interesting. Even a post graduate student will truly benefit from this course.

Dozent

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Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

Über 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. ...

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