David Jerison received the A.B. from Harvard in 1975, and the Ph.D. from Princeton in 1980 under the direction of Elias Stein. Following an NSF postdoctoral fellowship at the University of Chicago, Professor Jerison joined the MIT mathematics faculty in 1981. His research is focussed on PDEs and Fourier analysis. He served as Chair of the Undergraduate Mathematics Committee, 1988-91, Chair of the Pure Mathematics Committee, 2002-04, and co-Chair of the Graduate Student Committee 2007-09. He is currently Chair of the Pure Mathematics Committee and directs SPUR, the mathematics department's summer undergraduate research program as well as the mathematics component of RSI (Research Science Institute) a summer science and engineering research program for high school students. A prior Sloan research fellow and Presidential Young Investigator, Professor Jerison was elected Fellow of the American Academy of Arts & Sciences in 1999. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship for a ten-year period.
Lecture 01: Derivatives, slope, velocity, rate of change
Lecture 02: Limits, continuity. Trigonometric limits.
Lecture 04: Chain rule. Higher derivatives.
Lecture 03: Derivatives of products, quotients, sine, cosine.
Lecture 05: Implicit differentiation, inverses.
Lecture 06: Exponential and log. Logarithmic differentiation; hyperbolic functions.
Lecture 07: Continuation and Review
Lecture 09: Linear and quadratic approximations
Lecture 10: Curve sketching
Lecture 11: Max-min problems
Lecture 12: Related rates
Lecture 13: Newton's method and other applications
Lecture 14: Mean value theorem; Inequalities
Lecture 15: Differentials, antiderivatives
Lecture 16: Differential equations, separation of variables
Lecture 18: Definite integrals
Lecture 19: First fundamental theorem of calculus
Lecture 20: Second fundamental theorem
Lecture 21: Applications to logarithms and geometry
Lecture 22: Volumes by disks and shells
Lecture 23: Work, average value, probability
Lecture 24: Numerical integration
Lecture 25: Exam 3 review
Lecture 27: Trigonometric integrals and substitution
Lecture 28: Integration by inverse substitution; completing the square use
Lecture 29: Partial fractions
Lecture 30: Integration by parts, reduction formulae
Lecture 31: Parametric equations, arclength, surface area
Lecture 32: Polar coordinates; area in polar coordinates
Lecture 33: Exam 4 review
Lecture 35: Indeterminate forms - L'Hôspital's rule
Lecture 36: Improper integrals
Lecture 37: Infinite series and convergence tests
Lecture 38: Taylor's series
Lecture 39: Final review