vector spaces
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Understanding the differential of a vector valued function.
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Using line integrals to find the work done on a particle moving through a vector field.
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Concrete example of the derivative of a vector valued function to better understand what it means.
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Using a position vector valued function to describe a curve or path.
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Expressing a vector as the scaled sum of unit vectors.
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Final Showdown, Thinking About Design, Runtime Performance, Memory Used, Code Complexity, Making Tradeoffs, Array vs Vector, Stack/Queue vs Vector, Set vs Sorted Vector, Pointer-based vs. Contiguous Memory, CS106B MVPs, Pointers, To Remember Years from Now, After CS106B, considering.cs
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Buffer: Vector vs Stack, Buffer as Linked List, Cursor Design, Use of Dummy Cell, Linked List Insert/delete, Linked List Cursor Movement, Compare Implementation, Doubly Linked List, Compare Implementation, Space Time Trade Off, Implementing Map, Simple Map Implementation: Vector, Map as Vector : Performance Implication, A Different Strategy
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The discussion of four-vector in relativity continues but this time the focus is on the energy-momentum of a particle. The invariance of the energy-momentum four-vector is due to the fact that rest mass of a particle is invariant under coordinate transformations.
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The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers). Likewise energy and momentum are unified into the energy-momentum four-vector.
