Free online courseCalculus 3

Course Description

Calculus 3 is an extensive course with a total duration of 75 hours and 24 minutes. Renowned for its depth and clarity, the course has earned an exceptional average rating of 5 out of 5 stars, reflecting its high-quality instruction and comprehensive content.

Belonging to the category of Basic Studies, specifically under Calculus, this course delves into advanced topics fundamental to understanding multidimensional spaces and multivariable calculus. It begins by introducing vectors and their application in a 3-D coordinate system, progressing to operations with vectors such as the dot product and cross product.

Students will learn to navigate 3-D space through lectures focused on lines, planes, and surfaces, including the use of cylindrical and spherical coordinates. This foundational knowledge sets the stage for exploring vector functions, their derivatives, integrals, and various applications like arc length and velocity.

The course offers a detailed examination of multivariable functions, addressing domain, continuity, partial derivatives, and the chain rule. Students will explore advanced concepts such as directional derivatives, gradients, tangent planes, normal lines, and optimization techniques including LaGrange Multipliers.

A significant portion of the course is dedicated to multiple integrals. Students are guided through double and triple integrals, including regions defined by polar, cylindrical, and spherical coordinates. Practical applications such as finding the center of mass and volume are thoroughly covered.

Finally, the course introduces vector fields, including divergence, curl, and the computation of line integrals over both conservative and non-conservative fields. Advanced theorems like Green's Theorem, and Divergence/Stokes' Theorem are also explored, solidifying students' understanding of the complex interplay between calculus and vector analysis.

Calculus 3 stands out for its methodical approach and the depth of topics covered, making it an invaluable resource for anyone seeking to master multivariable calculus.