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

2. The Original Theoretical Minimum Theoretical Minimum: Overview 2 Lev Davidovich Landau, 1908 - 1968 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.

3. Our Theoretical Minimum Theoretical Minimum: Overview 3 Leonard Susskind, 1940- 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

4. 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

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

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

7. Vector Components Spaces, Trigonometry, and Vectors 7

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

9. Units Particle Motion (Kinematics) 9

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

11. Limits Differential Calculus 11 

12. What Have We Done? Differential Calculus 12 

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

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

15. Animatedly Integral Calculus 15

16. At Any Given Level Integral Calculus 16

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

18. General Dynamics Dynamics 18

19. Isaac Newton Dynamics 19 1642-1727 Philosophiæ Naturalis Principia Mathematica

20. Newtonian Dynamics Dynamics 20

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

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

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

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

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

26. Formulating (cont.) Least Action 26

27. Least Action 27

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

29. 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