Mean Value Theorem

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From a channel Lumen includes in full: MathDoctorBob, a maths professor, has a large archive of complete course lectures in algebra, calculus, linear algebra and abstract algebra, plus research talks.

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A 8-minute video from MathDoctorBob's catalogue; the title names its topic.

Science & Math

Video by MathDoctorBob, played through YouTube's embedded player.

Part of Calculus Pt 1: Limits and Derivatives

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Approximating with Taylor Polynomials

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A 4-minute video from MathDoctorBob's catalogue; the title names its topic.

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BAG1.2. Toric Varieties 2 - Affine Toric Varieties

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A 19-minute video from MathDoctorBob's catalogue; the title names its topic.

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Builds up what a neural network actually is — neurons as numbers, layers, weights and biases — using handwritten-digit recognition as the running example.

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A visual introduction to the Fourier transform: winding a signal around a circle to find its frequencies.

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Gilbert Strang's first lecture of MIT 18.06: the geometry of linear equations.

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Gödel's incompleteness, Turing's halting problem and the limits of mathematics.

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Bell Labs' J.N. Shive uses a mechanical wave machine to show reflection, standing waves, resonance and impedance matching — the ideas behind transmission lines.

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Entropy, the arrow of time and why the Sun is a source of low entropy rather than just energy.

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MIT 8.04 Quantum Physics I, lecture 1: superposition, introduced through experiments with 'hardness' and 'color'.

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CuriousMarc opens an HP 5061A caesium beam clock and explains, module by module, how it locks to an atomic transition.

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Boeing aerodynamicist Doug McLean dismantles popular wrong explanations of lift and explains what really happens.

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How Julius Caesar's calendar reform produced the 445-day year of 46 BCE and gave us the Julian calendar.