The Probem of Motion and the Methods to Solve It to be a Great Amateur Theoretical Physicist

This course develops the Newtonian theory of mechanics, it also develops relevant ideas from calculus, linear algebra, multivariable calculus, and ordinary differential equations. Along the way I will also introduce Mathematica and how to use it to solve problems in mechanics (such sections are optional for those who have Mathematica).

For what follows these are good resources:

• Feynman, Lieghton, Sands, The Feynman Lectures on Physics volume 1, Now available for online reading at: http://www.feynmanlectures.caltech.edu/I_toc_sc.html.

If you wish to buy a book, I recommend these:

• Frank Blume, Calvin Piston, (2014), Applied Calculus for Scientists and Engineers, Volumes 1 and 2. Available at Amazon.com.
• Richard P. Feynman, Robert B. Leighton, Matthew Sands, (2011), The Feynman Lectures on Physics, vol. 1. Basic Books
• R. Shankar, (2014), Fundamentals of Physics Mechanics, Relativity, and Thermodynmaics. Yale University Press.
• Leonard Susskind, George E. Hrabovsky, (2013), The Theoretical Minimum. Basic Books.

This requires either Mathematica 8 or later, or the free Mathematica CDF Viewer, though the viewer cannot run the programs, (you can find that here). You will also need to download the MAST Writing Style into the folder SystemFiles/Front End/Stylesheets. You can download that here. Once you load this file into the folder rename it MAST Writing Style 3. Reload Mathematica and it will be there.

I am assuming that you have completed studying all of Basic Mathematics and Physics and possibly Basic Ideas of Mathematica.

1. The Problem of Motion
2. Review of Dynamical Systems
3. Review of Motion in One Dimension
4. Review of Vectors
5. Characterizing the State Space of Classical Mechanics
6. Calculus of Vector Functions of a Scalar Variable
7. Kinematics in More Than One Dimension
8. General Orthogonal Curvilinear Coordinates
9. The Kinematical Equations of Motion
10. Galilean Relativity
11. Forces and Mass
12. Forces in Equilibrium
13. The Program of Newtonian Classical Mechanics
14. Setting Up Newton's Equation of Motion in More Than One Dimension
15. Solving Newton's Equations of Motion
16. Curves in Space
17. Scalar-Valued Functions of Many Variables and Partial Derivatives
18. Line Integrals
19. Work and Power
20. Kinetic Energy
21. Potential Energy and Force
22. Equilibrium
23. The Harmonic Oscillator
24. Damping and Forcing of Oscillations
25. The Conservation of Energy
26. Virtual Displacement and Virtual Work
27. Systems of More Than One Particle
28. The Calculus of Variations
29. The Principle of Stationary Action
30. The Euler-Lagrange Equation
31. Translation Invariance and Momentum Conservation
32. Accretion and Decay
33. Collisions and Scattering
34. Rotation Invariance and Conservation of Angular Momentum
35. Motion in Accelerated Frames
36. Rotating Systems
37. Rigid Bodies
38. Tensor Algebra
39. Moment of Inertia
40. Gyrodynamics

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