Where We’ve Been tell them what you told them 1 A Trip Down Memory Lane.

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Presentation transcript:

Where We’ve Been tell them what you told them 1 A Trip Down Memory Lane

The Original Theoretical Minimum Theoretical Minimum: Overview 2 Lev Davidovich Landau, One of the great Russian physicists of the 20 th century Tested prospective students in theoretical physics. 43 students passed, the 2 nd of whom was his famous collaborator, Ilya Lifshitz.

Our Theoretical Minimum Theoretical Minimum: Overview 3 Leonard Susskind, Prominent American physicist at Stanford University: “brilliant imagination and originality” Received many awards and honors (but not yet The Big One) Devotes substantial efforts to a series of lectures aimed at the physics-oriented public

Susskind’s Target Audience “The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.” Theoretical Minimum: Overview 4

Principal Elements (1) State Model of Physics Laws Determinism Reversibility Allowed vs Disallowed Forms Theoretical Minimum: Overview 5

Mathematical Infrastructure (I) Spaces Trigonometry Vectors Principal Elements (2) Theoretical Minimum: Overview 6 x y z

Vector Components Spaces, Trigonometry, and Vectors 7

Principal Elements (3) Description of motion (kinematics) Where particles move but not why: position velocity (and speed) acceleration Theoretical Minimum: Overview 8

Units Particle Motion (Kinematics) 9

Principal Elements (3.5) Mathematical Infrastructure (III) Differential calculus Theoretical Minimum: Overview 10

Limits Differential Calculus 11 

What Have We Done? Differential Calculus 12 

Principal Elements (4) Mathematical Infrastructure (IV) Integral calculus Theoretical Minimum: Overview 13

Goal Compute the signed area under some portion of an arbitrary curve Integral Calculus 14

Animatedly Integral Calculus 15

At Any Given Level Integral Calculus 16

Principal Elements (5) Dynamics of motion Forces and their effects Theoretical Minimum: Overview 17

General Dynamics Dynamics 18

Isaac Newton Dynamics Philosophiæ Naturalis Principia Mathematica

Newtonian Dynamics Dynamics 20

An Aside on Units Fundamental units are Dynamics 21 UnitMeasured in… Lengthmeters Timeseconds Masskilograms

Units of Observed Quantities QuantityUnitsMeasured in… positionmeters velocitymeters/second accelerationmeters/second 2 forcekilogram-meters/second 2 Dynamics 22

Principal Elements (6) Mathematical Infrastructure (V) Partial differentiation (just more differentiation) Theoretical Minimum: Overview 23

Conservation of Energy We have shown that conservative forces always conserve energy. Energy 24

Principal Elements (7) Extremum principles the whole rest of the course the Promised Land the heart of classical mechanics Theoretical Minimum: Overview 25

Formulating (cont.) Least Action 26

Least Action 27

Principal Elements (7.1) Theoretical Minimum: Overview 28 Example: Lagrangian Mechanics

So What’s the Point? Lagrangian bundles everything about a system’s dynamics into one package. Very straight-forward to change coordinates, a common operation. Easy to work out equations of motion for complex problems by routine differentiation. Least Action 29