Vector Calculus for Engineers

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.