
Explore the multi-variable calculus module of the GRE subject math prep, a modular course spanning basic single-variable calculus, multivariable calculus, differential equations, linear algebra, and abstract algebra.
Explore vectors in R^3, including points, arrows, and the standard basis i, j, k. Apply addition, subtraction, scalar multiplication, dot product, projection, unit vectors, normals, and plane and line equations.
Compute the cross product to get a normal perpendicular to two vectors, using the determinant with i, j, k; relate its length to area and the triple product to volume.
Learn partial derivatives f_x and f_y for two-variable functions, understand the gradient as the direction of rate of change, and apply tangent planes and linear approximation via the chain rule.
Explore min-max problems in multivariable calculus by locating local and global extrema via the gradient and second derivative tests, then solve constrained optimization with Lagrange multipliers and boundary analysis.
Parametrize curves to compute line integrals of the first and second kinds, and apply double integrals, polar coordinates with the Jacobian, work, and Green's theorem for volumes and closed curves.
Take the final quiz for module 4 multivariable calculus, with a few questions appearing for two and a half minutes each; pace yourself and use the next lecture for answers.
Explore multivariable calculus techniques for optimization and line integrals: compute angles via dot product of normal vectors, apply Lagrange multipliers, use parametrization of boundaries, and verify results with Green's theorem.
Explore practice exams, study plans, and handouts to master multivariable calculus for the GRE subject math exam. Join the mailing list and online community for updates and expert solutions.
This course is a prep course for the GRE Subject exam in Mathematics. If you wish to apply for a grad program in math, statistics and such, this exam is required.
This is the forth module and includes all the multivariable calculus material needed in order to excel in the exam. More importantly, the course teaches techniques for solving problems FAST (since in the exam you will have 2.5 min per question - very little time).
We will go over the following topics:
The course is designed to review all that is necessary to get you up to speed and get you solving real exam problems. Content covered in the previous modules is assumed.
See the free intro lecture to get more details.
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