All meetings are in Room 2-132.
Week 1: MTWR, June 4 - June 7, 9AM - 12:30 PM. There is no class Friday!
Weeks 2-6: MTWRF, June 11 - July 13, 12:30 - 2:30 PM. There is no class on July 4th!
Tudor Padurariu (tpad(at)mit.edu)
Kevin Sackel (ksackel(at)mit.edu)
Syllabus (NB: The outline in the syllabus is tentative, and there is no class July 4th.)
Previous summers: 2009, 2013, 2015
Supplementary notes: Single Variable 18.01, Multi-variable 18.02
Room 2-242
Week 1: MTWR 1:30 PM - 2:30 PM
Weeks 2-3: WR 10:30 AM - 11:30 AM
Weeks 4-6: W 11:00-11:30 AM, R 9:30 AM - 11:30 AM
PSet 0 (no need to hand in!), Solutions
PSet 1, due Friday, June 15, Solutions
PSet 2, due Friday, June 22, Solutions
PSet 3, due Friday, June 29, Solutions
PSet 4, due Friday, July 6, Solutions
PSet 5, due Friday, July 13, Solutions
Exam 1, due Monday, June 11, Solutions
Exam 2, due Monday, July 2, Solutions
Exam 3, due Monday, July 16, Solutions
Lecture 1 (Monday, June 4): Continuous functions; differentiation, computing the slope of the tangent line at a given point on y = f(x); properties of differentiation - linearity, product rule, chain rule, quotient rule, derivative of x^n, higher derivatives; using the first and second derivative to graph a function in the xy-plane, critical points, the second derivative test; max-min problems; implicit differentiation.
Lecture 2 (Tuesday, June 5): Exponential, logarithm, and their derivatives, the constant e; trigonometric functions and their derivatives; linear approximation, fundamental limits, l'Hopital rule, examples; also Extra problems.
Lecture 3 (Wednesday, June 6): Fundamental problems from antiquity, Archimedes solution to computing areas, Fundamental Theorem of Calculus, antiderivatives, examples of antiderivatives, techniques for computing antiderivatives: substitution, partial fractions, and integration by parts.
Lecture 4 (Thursday, June 7): Computing the length of a curve; computing volumes by the disk and shell methods; surface areas, examples; indefinite integrals, comparison test; infinite series, convergence and divergence, exercises.
Lecture 5 (Monday, June 11): More on infinite series, the integral test, alternating series test, the root and ratio tests; powers series: examples, radius of convergence, basic operations, Taylor series, examples.
Lecture 6 (Tuesday, June 12): Vectors, addition, multiplication by a scalar, dot product, cross product, geometric significance, geometric applications.
Lecture 7 (Wednesday, June 13): Determinants of 2x2 and 3x3 matrices; lines in 2D space, lines and planes in 3D space: parametric and implicit equations.
Lecture 8 (Thursday, June 14): Curves in 2D and 3D space: parametric and implicit equations, velocity, speed, tangent vector, acceleration, curvature.
Lecture 9 (Friday, June 15): Examples of parametrized curves; 2D polar coordinates; going from cartesian to polar coordinates and back.
Lecture 10 (Monday, June 18): Graphs of functions of two variables, equation of the tangent plane at a point on the graph of a function of two variables, partial derivatives, tangent plane approximation, vector fields, gradients for functions of two variables.
Lecture 11 (Tuesday, June 19): Gradients for functions in three variables, the gradient is normal to level sets, equation of the tangent plane to a level surface f(x,y,z)=c, directional derivatives, further properties of the gradient.
Lecture 12 (Wednesday, June 20): Second derivative test for functions of two variables, distance between two lines in the space, method of least squares.
Lecture 13 (Thursday, June 21): Lagrange multipliers and examples, chain rule and examples.
Lecture 14 (Friday, June 22): Applications of Lagrange multipliers: AM- GM, Cobb-Douglas, Snell's Law; applications of the chain rule: Laplace equation, examples of harmonic functions.
Lecture 15 (Monday, June 25): Double integrals; finding volume; vertical and horizontal strips; writing down bounds; switching order of integration; mass; center of mass.
Lecture 16 (Tuesday, June 26): Integration in polar coordinates; double integrals for general coordinates.
Lecture 17 (Wednesday, June 27): More double integrals in general coordinates; Mamikon's Theorem; integrating (sin(x))^a*(cos(x))^b; triple integrals; cylindrical coordinates.
Lecture 18 (Thursday, June 28): Moment of inertia; spherical coordinates; integrating in spherical coordinates.
Lecture 19 (Friday, June 29): Line integrals (2D + 3D); parametrization independence and an example (fixed from lecture); Fundamental Theorem of Calculus for line integrals; gradient fields; conservative/path-independent fields.
Lecture 20 (Monday, July 2): Curl (2D); Green's Theorem (tangential form); equivalence of gradient, conservative, and curl-free vector fields; computing potential functions.
Lecture 21 (Tuesday, July 3): Examples of Green's Theorem; proof of Green's Theorem.
Lecture 22 (Thursday, July 5): Flux (2D); Green's Theorem (normal form); extensions of Green's Theorem, e.g. to multiply-connected domains; physical interpretation of div and curl (2D).
Lecture 23 (Friday, July 6): Surface integrals for graphs, cylindrical, and spherical surfaces; flux (3D).
Lecture 24 (Monday, July 9): Parametrized surfaces; flux for parametrized surfaces; divergence (3D); the divergence theorem.
Lecture 25 (Tuesday, July 10): Curl (3D); Stokes' Theorem; gradient, conservative, and curl-free vector fields (3D).
Lecture 26 (Wednesday, July 11): Physical interpretations of div and curl; relations of div, grad, and curl; review of Stokes-type theorems (Fundamental Theorem of Calculus, Green's Theorem, divergence theorem, Stokes' Theorem).
Lecture 27 (Thursday, July 12): (Finishing Lecture 26, see previous notes); polar planimeter and demonstration; Maxwell's Equations.
Lecture 28 (Friday, July 13): Extra topics, TBD (non-examinable).