Calculus 1B: Integration
offered by MIT University

Private University
168 acre campus
Estd. 1861

Calculus 1B: Integration
at
MIT University
Overview

Gain a comprehensive overview of Calculus 1B: Integration

Duration	15 weeks
Total fee	₹8,281
Mode of learning	Online
Course Level	UG Certificate

Calculus 1B: Integration
at
MIT University
Highlights

Earn a certificate after completion

Calculus 1B: Integration
at
MIT University
Course details

What are the course deliverables?

Some differential equation models for physical phenomena and solutions
The geometric interpretation of the integral as an area under a graph, and the physical meaning as an accumulation
The connection of the integral to the derivative
Several methods of numerically and symbolically integrating function
To apply integrals to solve real world problems

More about this course

It focuses on the concept of integration, which is one of the fundamental techniques in calculus. Integration is used to determine the area under curves, compute accumulated quantities, and solve a wide range of mathematical and real-world problems
You will learn to interpret it geometrically as an area under a curve, and discover its connection to the derivative
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

Calculus 1B: Integration
at
MIT University
Curriculum

Modeling the Integral

Differentials and Antiderivatives

Differential Equations

Separation of Variables

Theory of Integration

Mean Value Theorem

Definition of the Integral and the First Fundamental Theorem

Second Fundamental Theorem

Applications

Areas and Volumes

Average Value and Probability

Arc Length and Surface Area

Techniques of Integration

Numerical Integration

Trigonometric Powers, Trig Substitutions, Completing the Square

Partial Fractions, Integration by Parts

Calculus 1B: Integration
at
MIT University
Faculty details

David Jerison

David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis. Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each

Gigliola Staffilani

Gigliola Staffilani is the Abby Rockefeller Mauzé Professor of Mathematics since 2007, and Associate Department Head as of July 2013. She received the B.S. equivalent from the University of Bologna in 1989, and the S.M. and Ph.D. degrees from the University of Chicago in 1991 and 95. Carlos Kenig was her doctoral advisor. Following a Szegö Assistant Professorship at Stanford, she had faculty appointments at Stanford, Princeton and Brown (tenured at Stanford and Brown), before joining the MIT mathematics faculty in 2002 as tenured associate professor (professor in 2006). Professor Staffilani is an analyst, with a concentration on dispersive nonlinear PDEs. At Stanford, she received the Harold M. Bacon Memorial Teaching Award in 1997, and was given the Frederick E. Terman Award for young faculty in 1998. She was a Sloan fellow from 2000-02. Professor Staffilani served as co-chair of the Graduate Student Committee in Pure Mathematics from 2009-2013. In 2013 she was elected member of the Massachusetts Academy of Science and a fellow of the AMS, and in 2014 fellow of the American Academy of Arts and Sciences.