Calculus 1C: Coordinate Systems & Infinite Series
Master the calculus of curves and coordinate systems; approximate functions with polynomials and infinite series. Part 3 of 3.
Calculus 1C: Coordinate Systems & Infinite Series
Master the calculus of curves and coordinate systems; approximate functions with polynomials and infinite series. Part 3 of 3.
How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.
What you'll learn
- To compute arc length
- To do calculus in polar coordinates
- Methods for parameterizing curves, and using the parameterizations to solve problems
- How to approximate functions with Taylor polynomials and series
- To determine convergence properties of infinite series
Prerequisites
- 18.01.1x Calculus 1A: Differentiation
- 18.01.2x Calculus 1B: Integration
Meet your instructors
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Professor of Mathematics -
Abby Rockefeller Mauze Professor -
Lecturer in Mathematics -
MITx Digital Learning Scientist, Statistics & Data Science MicroMasters Program
David Jerison
David Jerison
Professor of Mathematics
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
Abby Rockefeller Mauze Professor
Gigliola Staffilani is the Abby Rockefeller Mauzé Professor of Mathematics since 2007, and was Associate Department Head from July 2013 to 2015. She received the B.S. equivalent from the University of Bologna in 1989, and the M.S. 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 Sloan fellow from 2000-02, a member of the Institute for Advanced Study, in Princeton, NJ in 1996 and 2003 and a member of the Radcliffe Institute for Advanced Study at Harvard University in 2010.
At MIT Professor Staffilani served as co-chair of the Graduate Student Committee in Pure Mathematics from 2009-2013, and is the Faculty Diversity Officer since 2015. In 2013 she was elected member of the Massachusetts Academy of Science and a fellow of the AMS, and in 2014 member of the American Academy of Arts and Sciences. In 2017 she received a Guggenheim fellowship and a Simons Fellowship in Mathematics.
Jennifer French
Jennifer French
Lecturer in Mathematics
Jen French worked on developing online educational math content for 10 years with the MIT Department of mathematics. In that time she developed 10 MOOCs, several interactive visualizations, and a sketchResponse tool to enable instructors to auto grade student math sketches. She is currently teaching math in a first-year cohort at MIT called Concourse.
Karene Chu
Karene Chu
MITx Digital Learning Scientist, Statistics & Data Science MicroMasters Program
Karene Chu received her Ph.D. in mathematics from the University of Toronto in 2012. Since then she has been a postdoctoral fellow first at the University of Toronto/Fields Institute, and then at MIT, with research focus on knot theory. She has taught single and multi-variable calculus, and linear algebra at the University of Toronto where she received a teaching award.