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Are all vector fields the gradient of a potential? ... and the Helmholtz Decomposition
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Classroom Contents
Engineering Math - Vector Calculus and Partial Differential Equations
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- 1 Vector Calculus and Partial Differential Equations: Big Picture Overview
- 2 Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]
- 3 The Gradient Operator in Vector Calculus: Directions of Fastest Change & the Directional Derivative
- 4 The Divergence of a Vector Field: Sources and Sinks
- 5 The Curl of a Vector Field: Measuring Rotation
- 6 Gauss's Divergence Theorem
- 7 The Continuity Equation: A PDE for Mass Conservation, from Gauss's Divergence Theorem
- 8 Stokes' Theorem and Green's Theorem
- 9 Are all vector fields the gradient of a potential? ... and the Helmholtz Decomposition
- 10 Laplace's Equation and Potential Flow
- 11 Potential Flow Part 2: Details and Examples
- 12 Partial Differential Equations Overview
- 13 Laplace's Equation and Poisson's Equation
- 14 Deriving the Heat Equation: A Parabolic Partial Differential Equation for Heat Energy Conservation
- 15 The Heat Equation and the Steady State Heat Distribution via Laplace's Equation
- 16 Deriving the Heat Equation in 2D & 3D (& in N Dimensions!) with Control Volumes and Vector Calculus
- 17 PDE 101: Separation of Variables! ...or how I learned to stop worrying and solve Laplace's equation
- 18 Deriving the Wave Equation
- 19 Solving the Wave Equation with Separation of Variables... and Guitar String Physics
- 20 The Method of Characteristics and the Wave Equation
- 21 The Wave Equation and Slack Line Physics
- 22 Solving PDEs with the Laplace Transform: The Heat Equation
- 23 Solving PDEs with the Laplace Transform: The Wave Equation
