Ordinary differential equations
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This lecture explains what an economic model is, and why it allows for counterfactual reasoning and often yields paradoxical conclusions. Typically, equilibrium is defined as the solution to a system of simultaneous equations. The most important economic model is that of supply and demand in one market, which was understood to some extent by the ancient Greeks and even by Shakespeare. That model accurately fits the experiment from the last...more
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Manipulator Control, PD Control Stability, Task Oriented Control, Task Oriented Equations of Motion, Operational Space Dynamics, Example, Nonlinear Dynamic Decoupling, Trajectory Tracking
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Professor Channing Robertson of the Stanford University Chemical Engineering Department discusses balancing equations and the conservation of mass in relation to process design.
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After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger's three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical "Chladni" figures show how nodal patterns relate to frequencies. The analog...more
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Advice for Applying Machine Learning, Debugging Reinforcement Learning (RL) Algorithm, Linear Quadratic Regularization (LQR), Differential Dynamic Programming (DDP), Kalman Filter & Linear Quadratic Gaussian (LQG), Predict/update Steps of Kalman Filter, Linear Quadratic Gaussian (LQG)
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2 more examples of solving equations using the quadratic equation.
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U02_L1_T2_we1 : Solving Equations with the Distributive Property.
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U02_L1_T1_we2: Solving Equations 2.
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U02_L1_T1_we1: Solving Equations 1.
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Joint Space Dynamics, Newton-Euler Algorithm, Inertia Tensor, Example, Newton-Euler Equations, Lagrange Equations, Equations of Motion
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Introduction to basic algebraic equations of the form Ax=B.
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Equations with the variable on both sides.
