Factorization into A = LU
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Independence, Basis, and Dimension
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Vectors - Dot Products - Cross Products - 3D Kinematics
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Solving Ax = 0: Pivot Variables, Special Solutions
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Work - Kinetic Energy - Potential Energy - Conservative Forces - Conservation of Mechanical Energy - Newton's Law of Universal Gravitation
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Elimination with Matrices
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Powers of Ten - Units - Dimensions - Measurements - Uncertainties - Dimensional Analysis - Scaling Arguments
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Column Space and Nullspace
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Orthogonal Vectors and Subspaces
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Electric Field
Field Lines
Superposition
Inductive Charging
Dipoles
Induced Dipoles
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What holds our world together?
Electric Charges (Historical)
Polarization
Electric Force
Coulomb's Law
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Friction
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1D Kinematics - Speed - Velocity - Acceleration
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Solving First-order Linear ODE's; Steady-state and Transient Solutions.
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Projections onto Subspaces
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Rolling Motion - Gyroscopes - VERY NON-INTUITIVE
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The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.
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Introduction and lumped abstraction
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Eigenvalues and Eigenvectors
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Hooke's Law - Springs - Simple Harmonic Motion - Pendulum - Small Angle Approximation
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Basic circuit analysis method (KVL and KCL mMethod)
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Circular Motion - Centrifuges Moving - Reference Frames - Perceived Gravity
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First-order Substitution Methods: Bernouilli and Homogeneous ODE's.
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The Geometry of Linear Equations
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