Multivariable Calculus 1: Vectors and Derivatives
We live in a multivariable world. Explore the derivative in higher dimensions and learn how to apply it to solve real world problems. Part 1 of 3.
Multivariable Calculus 1: Vectors and Derivatives
We live in a multivariable world. Explore the derivative in higher dimensions and learn how to apply it to solve real world problems. Part 1 of 3.
Variables are all around us: temperature, altitude, location, profit, color, and countless others. Multivariable Calculus is the tool of choice to shed light on complex relationships between 2, 3, or hundreds of variables simultaneously.
What you'll learn
- How to visualize functions of 2 and 3 variables using level curves and level surfaces
- How to compute partial derivatives, directional derivatives, and gradients
- How to optimize multivariable functions subject to constraint equations
- How to represent the linear approximation of a multivariable function using vectors and matrices.
Prerequisites
Meet your instructors
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Claude Shannon Professor of Mathematics MacVicar Faculty Fellow -
Herchel Smith Professor of Mathematics, Harvard University -
Lecturer in Mathematics
Lawrence Guth
Lawrence Guth
Claude Shannon Professor of Mathematics MacVicar Faculty Fellow
Larry Guth is a Professor of Mathematics at MIT. He received the Bocher prize from the American Mathematical Society and the Maryam Mirzakhani prize from the National Academy of Science. He works on problems in geometry related to isoperimetric inequalities and problems in Fourier analysis. He taught 18.02 four times between 2017 and 2020.
Areas of expertise: Metric geometry, harmonic analysis, extremal combinatorics
Denis Auroux
Denis Auroux
Herchel Smith Professor of Mathematics, Harvard University
Denis Auroux completed his studies in France, where he obtained his PhD in 1999 from Ecole Polytechnique. After his PhD he moved to MIT where he was a Moore Instructor from 1999 to 2002, an Assistant Professor of Mathematics from 2002 to 2004, and an Associate Professor from 2004 to 2009, before moving to UC Berkeley in 2009 and then to Harvard University in 2018. His research work is in the field of symplectic geometry, with a particular focus on the homological mirror symmetry conjecture. Prof. Auroux taught 18.02 five times from 2003 to 2008, including the Fall 2007 lectures which were filmed and preserved for posterity by MIT's OpenCourseWare project.
Denis Auroux Photo Credit: George Bergman
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.