This is the site of the Concourse 18.01A-02A course (a.k.a. CC.181a and CC.182a) that ran for 8 years from Fall 2011 through Fall 2018. Some version of this course may at some point again be offered within the remnants of the Concourse Program, a program that billed itself as “integrating science and the humanities” but which made no effort to actually do so for at least the last 8 years. Concourse has sold that false bill of goods simply to justify its continued existence as an MIT Freshman Learning Community.

The students of Concourse are much the same as virtually all MIT students - curious, smart, and a pleasure to know. The Concourse Program, in contrast, is built on a foundation of hypocrisy. Themes like justice and truth and knowledge are presented to its students, but what has come to define Concourse are the need for control and enforcing obedience and taking care of the selfish needs of the administrators of the program. Those of us who were simply very good at teaching our courses (and greatly appreciated by our students) and who did our best to actually integrate science and the humanities or, in my case, civic responsibility, have never been valued by the directors of the program. Those who teach in Concourse actually have very little say in how the program operates, and the program has largely been on auto-pilot for some time. That said, you could probably randomly pick 50 MIT freshmen and make it work as long as good teachers were in the program who actively engaged students.

I treasure all of my relationships with students built up over 9 years working in Concourse as well as the absolute joy of sharing an office for most of my time there with a truly wonderful teacher of Chemistry and mentor of students. I miss the students more than I can put into words. However, I don’t at all miss working an an oppressive environment with an incompetent and vengeful Assistant Director and a Director who values only blind obedience and who would gladly throw under the bus anyone whose independence in any way threatened her personal insecurities. Any academic program, including any MIT Freshman Learning Community, should aspire to greater things. - Robert Winters

18.01A Topics:

• Review of basic ideas of Differential Calculus. (Chaps. 2-7)
• Applications of Integration: area, volume, volume of solids of revolution, arclength, area of a surface of revolution, work and energy, hydrostatic force. (Chap. 7)
• Techniques of integration: substitution, trigonometric integrals, trigonometric substitutions, partial fractions, integration by parts, miscellaneous methods, numerical integration and Simpson's Rule. (Chap. 10)
• Further Applications of Integration: Center of mass, centroids, moment of inertia. (Chap. 11)
• Indeterminate forms, L’Hôpital's Rule, improper integrals.
• Sequences, infinite series, convergent vs. divergent series, comparison tests, integral test, ratio and root tests, alternating series, absolute vs. conditional convergence. (Chap. 13)
• Power series, interval of convergence, differentiation and integration of power series, Taylor Series and Taylor’s Formula, applications to differential equations. (Chap. 14)
• Probability. (Supplementary Notes)

18.02A Topics:

• Coordinates, vectors and vector algebra in R² and R³; dot product, cross product, projection, equations of lines and planes, matrix methods. (Chaps. 17-18 and Notes)
• Parametric equations of curves in R² and R³; coordinates, derivatives of vector-valued functions, velocity and acceleration, tangent vectors, arclength; curvature and unit normal vector, tangential and normal components of acceleration, Kepler’s Laws and Newton's Law of Gravitation. (Chaps. 17-18)
• Cylinders and surfaces of revolution, cylindrical and spherical coordinates; parameterized surfaces in R² and R³. (Chap. 18)
• Functions of several variables - limits, continuity, and differentiabilty; partial derivatives, gradients, linear approximation, directional derivatives, Chain Rule. (Chap. 19)
• Optimization - unconstrained and constrained; implicit functions and implicit differentiation. (Chap. 19)
• Multiple integrals, integration over regions in R² and R³ and their applications using Cartesian, polar, cylindrical, and spherical coordinates, gravitational attraction. (Chap. 20)
• Vector fields and their applications. (Notes)
• Integration over curves in R² and R³ by parameterization; work integrals, and applications; independence of path and conservative vector fields; Green’s Theorem. (Chap. 21)
• Integration over surfaces in R³ by parameterization - flux integrals, surface area, and applications. (Chap. 21)
• Calculus of vector fields; curl and divergence of vector fields; Stokes’ Theorem, Divergence Theorem; Maxwell’s equations. (Chap. 21)