Massachusetts Institute of Technology Online Course On Calculus

MIT in partnership with edX is offering a online course aims discover the integral-what it is and how to compute it. This course is intended to teach how to use calculus to model real world phenomena.

Course designs are aligned to make students learn to interpret integral geometrically as an area under a graph, and discover its connection to the derivative. The course will start on starts on  December 1, 2015.

Course At A Glance

Length: 11 weeks course
Effort:  5-10 hours total
Subject: Calculus 1B: Integration
Institution: Massachusetts Institute of Technology & edX. This course was funded in part by the Wertheimer Fund.
Languages: English
Price:  Free
Certificate Available: Yes. Verified Certificate for $ 100
Session:  Starts on December 1, 2015.

Providers Details

Massachusetts Institute of Technology — a coeducational, privately endowed research university founded in 1861 — is dedicated to advancing knowledge and educating students in science, technology, and other areas of scholarship that will best serve the nation and the world in the 21st century.

This online platform edX provides online courses from the world’s best universities. edX can empower you to build innovative applications, services, and experiences on the HarvardX platform that will help you make a meaningful impact in today’s interconnected world.

About This Course

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative.  You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

Why Take This Course?

This is a free online course. This MOOC will be offered with Video Transcripts.  No prior experience is required. Applicants can also get Verified Certificate. Prerequisites are

18.01.1x Calculus 1A – Differentiation.

Course Syllabus

  1. Modeling the Integral

-Differentials and Antiderivatives
-Differential Equations
-Separation of Variables

  1. Theory of Integration

-Mean Value Theorem
-Definition of the Integral and the First Fundamental Theorem
-Second Fundamental Theorem

  1. Applications

-Areas and Volumes

-Average Value and Probability
-Arc Length and Surface Area

  1. Techniques of Integration

-Numerical Integration
-Trigonometric Powers, Trig Substitutions, Completing the Square
-Partial Fractions, Integration by Parts

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.

This course was funded in part by the Wertheimer Fund.

Learning Outcomes

After completing this course you will have knowledge of :
-Some differential equation models for physical phenomena and solutions
-The geometric interpretation, and physical meaning of the integral
-The connection of the integral to the derivative
-Several methods of numerically and symbolically integrating functions
-To apply integrals to solve real world problems

Instructors

– David Jerison

Mathematics Faculty

-Gigliola Staffilani

An analyst, with a concentration on dispersive nonlinear PDEs.

-Jen French

MITx Digital Learning Scientist in the MIT math department.

-Stephen Wang

In fall 2015 he will join the Rice University mathematics faculty.

Requirements

-Prerequisites are 18.01.1x Calculus 1A – Differentiation

Detailed Information

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