Vector Calculus for Engineers

Explore a comprehensive video series on vector calculus tailored for engineers. Delve into essential topics including vectors, coordinate systems, vector operations, analytic geometry, scalar and vector fields, partial derivatives, gradient, divergence, curl, and Laplacian. Master double and triple integrals, polar coordinates, and coordinate transformations. Learn about line and surface integrals, flux integrals, and fundamental theorems like the gradient theorem, divergence theorem, and Stokes' theorem. Apply vector calculus concepts to real-world engineering problems, including electromagnetic waves and fluid dynamics. Gain a solid foundation in matrix operations as a supplementary skill. Through 53 lectures spanning 9 hours, develop the mathematical tools necessary for advanced engineering applications.

Promotional Video | Vector Calculus for Engineers.
Vectors | Lecture 1 | Vector Calculus for Engineers.
Cartesian coordinates | Lecture 2 | Vector Calculus for Engineers.
Dot product | Lecture 3 | Vector Calculus for Engineers.
Cross product | Lecture 4 | Vector Calculus for Engineers.
Analytic geometry of lines | Lecture 5 | Vector Calculus for Engineers.
Analytic geometry of planes | Lecture 6 | Vector Calculus for Engineers.
Kronecker delta and Levi-Civita symbol | Lecture 7 | Vector Calculus for Engineers.
Vector Identities | Lecture 8 | Vector Calculus for Engineers.
Scalar Triple Product | Lecture 9 | Vector Calculus for Engineers.
Vector Triple Product | Lecture 10 | Vector Calculus for Engineers.
Scalar and vector fields | Lecture 11 | Vector Calculus for Engineers.
Partial derivatives | Lecture 12 | Vector Calculus for Engineers.
Method of least squares | Lecture 13 | Vector Calculus for Engineers.
Multivariable chain rule | Lecture 14 | Vector Calculus for Engineers.
Triple product rule | Lecture 15 | Vector Calculus for Engineers.
Triple product rule: the ideal gas law | Lecture 16 | Vector Calculus for Engineers.
Gradient of a scalar field | Lecture 17 | Vector Calculus for Engineers.
Divergence of a vector field | Lecture 18 | Vector Calculus for Engineers.
Curl of a vector field | Lecture 19 | Vector Calculus for Engineers.
Laplacian of a scalar or vector field | Lecture 20 | Vector Calculus for Engineers.
Vector calculus identities | Lecture 21 | Vector Calculus for Engineers.
Divergence of the cross product of two vectors (proof) | Lecture 22 | Vector Calculus for Engineers.
Electromagnetic waves from Maxwell's equations | Lecture 23 | Vector Calculus for Engineers.
Double and triple integrals | Lecture 24 | Vector Calculus for Engineers.
Double integral over a triangular region | Lecture 25 | Vector Calculus for Engineers.
Polar Coordinates (Gradient) | Lecture 26 | Vector Calculus for Engineers.
Polar Coordinates (Divergence and Curl) | Lecture 27 | Vector Calculus for Engineers.
Polar Coordinates (Laplacian) | Lecture 28 | Vector Calculus for Engineers.
Central Force | Lecture 29 | Vector Calculus for Engineers.
Change of variables (single integral and substitution) | Lecture 30 | Vector Calculus for Engineers.
Change of variables (double integral and the Jacobian) | Lecture 31 | Vector Calculus for Engineers.
Cylindrical coordinates | Lecture 32 | Vector Calculus for Engineers.
Spherical coordinates (Part A) | Lecture 33 | Vector Calculus for Engineers.
The Del Operator in spherical coordinates | Lecture 34 | Vector Calculus for Engineers.
Line Integral of a Scalar Field | Lecture 35 | Vector Calculus for Engineers.
Arc Length: Perimeter of an Ellipse | Lecture 36 | Vector Calculus for Engineers.
Line Integral of a Vector Field | Lecture 37 | Vector Calculus for Engineers.
Work-Energy Theorem | Lecture 38 | Vector Calculus for Engineers.
Surface Integral of a Scalar Field | Lecture 39 | Vector Calculus for Engineers.
Surface Area of a Sphere | Lecture 40 | Vector Calculus for Engineers.
Surface Integral of a Vector Field | Lecture 41 | Vector Calculus for Engineers.
Flux Integrals | Lecture 42 | Vector Calculus for Engineers.
Gradient theorem | Lecture 43 | Vector Calculus for Engineers.
Conservative vector fields | Lecture 44 | Vector Calculus for Engineers.
Conservation of Energy | Lecture 45 | Vector Calculus for Engineers.
Divergence theorem | Lecture 46 | Vector Calculus for Engineers.
Divergence theorem (example in Cartesian coordinates) | Lecture 47 | Vector Calculus for Engineers.
Divergence theorem (example in spherical coordinates) | Lecture 48 | Vector Calculus for Engineers.
Derivation of the continuity equation of fluid dynamics | Lecture 49 | Vector Calculus for Engineers.
Green's theorem | Lecture 50 | Vector Calculus for Engineers.
Stokes' theorem from Green's theorem | Lecture 51 | Vector Calculus for Engineers.
Coordinate-free definition of the divergence and curl | Lecture 52 | Vector Calculus for Engineers.
Maxwell's equations from integral to differential form | Lecture 53 | Vector Calculus for Engineers.
Matrix addition & multiplication | Appendix A | Vector Calculus for Engineers.
Matrix determinants & inverses | Appendix B | Vector Calculus for Engineers.