vector spaces
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Preprocessing Commands - #Define as a Glorified Find and Replace, Preprocessing Macros - Preprocessor Commands With Arguments, Example of Macro Usage in the Vector assignment to Calculate the Address of the Nth Element, Assert Macro Implementation, How Asserts are Stripped Out for the Final Product Using #Ifdef and #Define, C Macro Drawbacks When Given More Complex Arguments, #Include as a Search and Replace Operation, < > Vs. " ", Output ...more
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Client Use of Templates, Vector Class, Vector Client Interface, Client Use of Vector, Type-safety in Templates, Grid Class, Grid Client Interface, Client Use of Grid, Stack Class, Stack Client Interface, Queue Class, Queue Client Interface, Client Use of Queue, Nested Templates, Learning a New API, CS106B Library Documentation
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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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Momentum and its conservation during collisions is introduced. Kinetic energy can decrease or increase during collisions. When kinetic energy is conserved, we call it an elastic collision. The momentum vector, internal forces, external forces and the conservation of momentum are discussed. Professor Lewin does some air track experiments where the released energy is from a compressed spring; kinetic energy increases but momentum is conserve...more
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This lecture is all about Newton's First (inertia), Second (F=ma) and Third (action=-reaction) Laws. He builds on past discussion of vector forces, moving on to decompose forces in the x and y directions. As the class comes to an end, Professor Lewin ends with a bizarre demo involving two identical strings, one suspending a mass, the other suspending from the mass. Which one breaks when you pull on the lower string, the upper string or t...more
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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.
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Professor Kleiner discusses two Roman cities in North Africa: Timgad and Leptis Magna. Timgad was created as an entirely new colony for Roman army veterans by Trajan in A.D. 100, and designed all at once as an ideal castrum plan. Leptis Magna, conversely, grew more gradually from its Carthaginian roots, experiencing significant Roman development under Augustus and Hadrian. Septimius Severus, the first Roman emperor from North Africa, was b...more
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
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