Calculus: Single Variable Part 3 - Integration

Instructor: Robert Ghrist

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4 modules

Gain insight into a topic and learn the fundamentals.

548 reviews

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

94%

Most learners liked this course

4 modules

Gain insight into a topic and learn the fundamentals.

548 reviews

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

94%

Most learners liked this course

Skills you'll gain

Details to know

Assessments

26 assignments

Taught in English

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There are 4 modules in 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.

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.

What's included

5 videos2 readings9 assignments

5 videos Total 75 minutes

Indefinite Integrals 17 minutes
A Simple O.D.E. 17 minutes
More O.D.E.s 16 minutes
O.D.E. Linearization 17 minutes
BONUS! 9 minutes

2 readings Total 20 minutes

How Grading Works 10 minutes
Your Guide to Getting Started in this Course 10 minutes

9 assignments Total 234 minutes

Learning Style Preference Survey 30 minutes
Challenge Homework: Indefinite Integrals 30 minutes
Challenge Homework: A Simple O.D.E. 30 minutes
Challenge Homework: More O.D.E.s 30 minutes
Challenge Homework: O.D.E. Linearization 30 minutes
Core Homework: Indefinite Integrals 30 minutes
Core Homework: A Simple O.D.E. 30 minutes
Core Homework: More O.D.E.s 10 minutes
Core Homework: O.D.E. Linearization 14 minutes

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.

What's included

6 videos8 assignments

6 videos Total 76 minutes

Integration by Substitution 14 minutes
Integration by Parts 17 minutes
Trig Substitution 15 minutes
BONUS! 7 minutes
Partial Fractions 16 minutes
BONUS! 7 minutes

8 assignments Total 170 minutes

Challenge Homework: Integration by Substitution 30 minutes
Challenge Homework: Integration by Parts 30 minutes
Challenge Homework: Trig Substitution 30 minutes
Challenge Homework: Partial Fractions 30 minutes
Core Homework: Integration by Substitution 12 minutes
Core Homework: Integration by Parts 14 minutes
Core Homework: Trig Substitution 12 minutes
Core Homework: Partial Fractions 12 minutes

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.

What's included

3 videos3 assignments

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.