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16. The Taylor Series and Other Mathematical Concepts

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16. The Taylor Series and Other Mathematical Concepts
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16
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24
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The lecture covers a number of mathematical concepts. The Taylor series is introduced and its properties discussed, supplemented by various examples. Complex numbers are explained in some detail, especially in their polar form. The lecture ends with a discussion of simple harmonic motion. 00:00 - Chapter 1. Derive Taylor Series of a Function, f as [Σ (0, ∞)fnxn/n!] 14:21 - Chapter 2. Examples of Functions with Invalid Taylor Series 17:30 - Chapter 3. Taylor Series for Popular Functions(cos x, ex,etc) 23:31 - Chapter 4. Derive Trigonometric Functions from Exponential Functions 31:41 - Chapter 5. Properties of Complex Numbers 42:40 - Chapter 6. Polar Form of Complex Numbers 50:04 - Chapter 7. Simple Harmonic Motions 01:03:07 - Chapter 8. Law of Conservation of Energy and Harmonic Motion Due to Torque
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ClockRulerSeries and parallel circuitsMassFahrgeschwindigkeitSpring (season)Power (physics)PunchingVideoFlugbahnNegativer WiderstandCaliperGas turbineTypesettingAmplitudeHypothetisches TeilchenBracket clockSpare partMeasurementLimiterAccelerationProjectileLinear motorForceShip naming and launchingRoots-type superchargerLecture/Conference
Cartridge (firearms)AmplitudePowder metallurgyRotationMassFACTS (newspaper)Angle of attackControl rodForceSingle (music)Roots-type superchargerPendulumBasis (linear algebra)Negativer WiderstandBending (metalworking)FahrgeschwindigkeitBird vocalizationCombined cycleSpare partPower (physics)DayHot workingSeries and parallel circuitsHyperbelnavigationDirect currentNanotechnologyDrehmassePower dividers and directional couplersStarOrbital periodCosmic distance ladderAnalog signalLecture/Conference
Electronic componentSchubvektorsteuerungOn-board diagnosticsAngle of attackNanotechnologyCaliperCardboard (paper product)Field-effect transistorRulerRing (jewellery)Spare partRoots-type superchargerMassStarBracket clockRoll formingShip classBending (metalworking)Continuous trackHot workingLecture/Conference
Control rodFACTS (newspaper)Newtonsche FlüssigkeitSpring (season)AmplitudeDayAngle of attackHomogeneous isotropic turbulenceThermodynamic equilibriumTypesettingGas turbineBending (metalworking)Angeregter ZustandHarmonicRoots-type superchargerCogenerationParticleRail transport operationsCapital shipMassAudio frequencyEngineFlavour (particle physics)Standard cellForceNegativer WiderstandCartridge (firearms)Field-effect transistorDirect currentRoll formingSpare partWednesdayHose couplingHot workingLecture/Conference
ScoutingMeasurementAntenna diversitySpring (season)ProjectileRoll formingNegativer WiderstandAudio frequencyShip naming and launchingAmplitudeMassFACTS (newspaper)FahrgeschwindigkeitClockOrbital periodSpare partForceMitsubishi A6M ZeroHarmonicGas turbineAccelerationCapital shipOn-board diagnosticsLecture/Conference
DrehmasseMassControl rodAngle of attackRoots-type superchargerFACTS (newspaper)Negativer WiderstandCosmic distance ladderSpare partHarmonicForceAudio feedbackPendulumFahrgeschwindigkeitDirect currentRotationRing (jewellery)Field-effect transistorEngine displacementBending (metalworking)Analog signalMagic (cryptography)AmplitudeOrbital periodLecture/Conference
Transcript: English(auto-generated)