UN 1205

Multivariable calculus: One to many multivariable functions, many to one, and many to many. Finding local maximum and minimum, Lagrange multipliers. Multivariable integration for one to many, many to one, and many to many functions, finding surface area, path integral, and volume. Divergence and Curl. Green's Theorem, Stokes Theorem and Divergence Theorem. Applying linear algebra to solve multivariable problems.

Multivariable Calculus concepts and comuptations and some logics behind each concept

Calculus in more dimensions; lines, graphs, surfaces, volumes. Vectors, matrixes, partial derivatives, change coordinate systems, double and triple integrals, stokes, divergence, curl.

Calculus I and II concepts in multivariable, including limits (parametrization), derivatives (gradient, curl, divergence, tangent and normal vectors), integrals (surface and curve integrals, Fubini, Stokes, Green, Divergence, and other relevant theorems), Taylor polynomials, and graphing; as well as fundamentals of linear algebra such as matrices, determinants, images, rank, and other matrix operations such as inner products or determinants. Additionally, we also breifly went over manifolds, Implicit Function Theorem, and Inverse Function Theorem.

Vector Fields, Multivariable derivatives & integrals, Stokes & Divergence Theorem, Basic Linear Algebra.

If you want to learn calculus and are comfortable with notation, take this course. If you don't care about math take another one.

Only recommend if existing background in calc 3 and basic understanding of linear algebra 1 Columbia University: Arts & Sciences Spring 2025 Course: UN1205 : Accelerated Multivariable Calculus-MATHUN1205_001_2025_1 - ACCELERATED MULTIVARIABLE CALC Instructor: Marco Castronovo