Vector Calculus
Dr. Trefor Bazett
Master vector calculus with Dr. Bazett! Learn multi-variable calculus, line integrals, and more. Excellent video course.
More resources on Vector Calculus
Vector Calculus Book (Free PDF)
OpenStax or similar free resources
Paul's Online Math Notes - Calc III
Comprehensive notes, examples, practice problems
Multivariable Calculus
Master vector calculus! Learn multivariable functions, partial derivatives, multiple integrals, and more.
Multivariable Calculus (18.02)
Master vector calculus with MIT's Multivariable Calculus (18.02) course. Learn from Auroux, Lewis, et al. and boost your math skills!
Vector Calculus for Engineers
This course covers both the theoretical foundations and practical applications of Vector Calculus. During the first week, students will learn about scalar and vector fields. In the second week, they will differentiate fields. The third week focuses on multidimensional integration and curvilinear coordinate systems. Line and surface integrals are covered in the fourth week, while the fifth week explores the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem, and Stokes' theorem. These theorems are essential for subjects in engineering such as Electromagnetism and Fluid Mechanics. Note that this course may also be referred to as Multivariable or Multivariate Calculus or Calculus 3 at some universities. A prerequisite for this course is two semesters of single-variable calculus (differentiation and integration). The course includes 53 concise lecture videos, each followed by a few problems to solve. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf Watch the promotional video from the link https://youtu.be/qUseabHb6Vk
mathworld.wolfram.com
MathWorld is an extensive online mathematics encyclopedia from Wolfram Research, offering rigorously written articles on a wide range of math topics. For vector calculus, it covers core concepts like gradient, divergence, and curl, as well as line and surface integrals and fundamental theorems (Green’s, Stokes’, and the Divergence theorem), with definitions, formulas, and worked examples.