MORE CALCULUS AT MIT

If you have gained competence in single variable calculus, and want to learn more, then you might try studying “Multivariable Calculus” from MIT. This course is taught by Professor Denis Auroux. The main focus here is on vector calculus and working with multiple variables. As is usual, you have access to transcripts, lecture notes, exams, and assignments in addition to the lecture videos.

This course includes the following topics: dot products, determinants, matrices, parametric equations, Kepler's Second Law, partial derivatives, least squares, second derivative test, chain rule, Lagrange Multipliers, partial differential equations, polar coordinates, change of variables, vector fields, path independence, flux, spherical coordinates, divergence theorem, line integrals, Stokes' Theorem, and Maxwell's Equations.

Multivariable Calculus (MIT)

CALCULUS AT MIT

This free course is called “Single Variable Calculus” and is taught by Professor David Jerison. It introduces students to differentiation of a single variable and integration. In addition to lecture videos there are transcripts, lecture notes, exams, and assignments available.

This course includes the following topics: rate of change, slope, limits, derivatives, chain rule, implicit differentiation, exponents, logarithms, hyperbolic functions, approximations, maxima, minima, Newton's Method, Mean Value Theorem, differential equations, definite integrals, fundamental theorems, work, probability, substitution, polar coordinates, infinite series, and Taylor series.

Single Variable Calculus (MIT)

INTRODUCTION TO PROGRAMMING AT MIT

This is a course from MIT's OpenCourseWare website. It is called “Introduction to Computer Science and Programming” and was instructed by Professors Eric Grimson and John Guttag. You can watch the lectures, read the transcripts, and view class assignments and exams. No programming experience is required. This course is intended to enable students to write small programs and use them for solving problems. The programming language utilized here is Python. Coincidentally, Python is the same language used by Blender.

This course includes the following topics: operators, variables, iteration, code patterns, recursion, bisection methods, lists, efficiency, algorithms, binary search, testing, debugging, dynamic programming, abstract data types, encapsulation, computational models, plotting, distributions, simulations, curve fitting, linear regression, and stock market simulation.

Intro. to Computer Sci. and Programming (MIT)

FIRST-CLASS PHYSICS TEACHER

Physics classes can be daunting and boring to many people. It is often hard to fully appreciate the utility, ingenuity, and elegance of using mathematics to explain how the real world works. Teaching physics effectively can be very difficult, but Walter Lewin makes it look easy. Dr. Lewin is a professor emeritus at Massachusetts Institute of Technology (MIT). Three courses taught by him have been recorded and made available online through MIT's OpenCourseWare project—much like Open Yale Courses. Anyone can access this university material for free, but do not expect college credit for watching the lectures. Dr. Lewin employs his comedic wit and dazzling demonstrations to clarify physics concepts and applications for his students. The first course is about “classical mechanics”, the second is about “electricity and magnetism”, and the third is about “vibrations and waves”. All three courses are intended for students who are experienced with calculus. Even if you do not plan on becoming a scientist, you will probably find the classes entertaining and thought-provoking.

The classical mechanics course includes the following topics: units, kinematics, vectors, circular motion, Newton's laws, friction, work, energy, forces, collisions, momentum, rotating bodies, stars, torque, oscillations, gravity, planetary orbits, gyroscopes, precession, fluid mechanics, buoyancy, harmonics, resonance, heat, thermodynamics, and astrophysics.

The electricity and magnetism course includes the following topics: historical background, fields, Gauss' law, flux, voltage, currents, EMF, circuits, electric motors, solenoids, induction, inductance, Faraday's law, eddy currents, levitation, material properties, electromagnets, Maxwell's equations, electromagnetic waves, light, refraction, polarization, scattering, rainbows, interference, Doppler effect, and cosmology.

The vibrations and waves course includes the following topics: oscillations, waves, damping, resonance, coupling, pendulum, sound, Fourier analysis, electromagnetic waves, polarization, Doppler effect, stars, radiation, reflection, standing waves, refraction, interference, double-slit experiment, thin films, diffraction, and rainbows.

Classical Mechanics (MIT)

Electricity & Magnetism (MIT)

Vibrations & Waves (MIT)