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