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Zen and the Art of Motorcycle Maintenance Robert Pirsig

Zen and the Art of Motorcycle Maintenance Robert Pirsig. The state of “ stuckness ” is to be treasured. It is the moment that precedes enlightenment. Differential equations. REVIEW. Algebraic equation : involves functions ; solutions are numbers.

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Zen and the Art of Motorcycle Maintenance Robert Pirsig

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  1. Zen and the Art of Motorcycle MaintenanceRobert Pirsig • The state of “stuckness” is to be treasured. It is the moment that precedes enlightenment.

  2. Differential equations REVIEW Algebraicequation: involves functions; solutions are numbers. Differential equation: involves derivatives; solutions are functions.

  3. Classification of ODEs Linearity: Homogeneity: Order:

  4. Superposition(linear, homogeneous equations) Can build a complex solution from the sum of two or more simpler solutions.

  5. Properties of the exponential function Taylor series: Sum rule: Power rule: Derivative Indefinite integral

  6. Wednesday Sept 15th: Univariate Calculus 3 Exponential, trigonometric, hyperbolic functions Differential eigenvalue problems F=ma for small oscillations

  7. Complex numbers The complex plane

  8. The complex exponential function

  9. Also:

  10. Hyperbolic functions

  11. Oscillations • Simple pendulum • Waves in water • Seismic waves • Iceberg or buoy • LC circuits • Milankovich cycles • Gyrotactic swimming current Swimming direction gravity

  12. Newton’s 2nd Law for Small Oscillations

  13. Newton’s 2nd Law for Small Oscillations

  14. Newton’s 2nd Law for Small Oscillations

  15. Newton’s 2nd Law for Small Oscillations Expand force about equilibrium point: =0 Small if x is small

  16. Newton’s 2nd Law for Small Oscillations =0 ~0

  17. Newton’s 2nd Law for Small Oscillations =0 ~0

  18. Angular frequency

  19. Pendulum

  20. Pendulum

  21. Pendulum

  22. All that matters:

  23. Differential eigenvalue problems

  24. Differential eigenvalue problems

  25. Differential eigenvalue problems

  26. Differential eigenvalue problems Zero crossings

  27. Differential eigenvalue problems Zero crossings

  28. Multivariate Calculus 1:multivariate functions,partial derivatives

  29. Partial derivatives Increment: x part y part

  30. Partial derivatives Could also be changing in time:

  31. Total derivatives x part y part t part

  32. Isocontours

  33. Isocontour examples

  34. Pacific watermasses

  35. Partial differential equations Algebraicequation: involves functions; solutions are numbers. Ordinary differential equation (ODE): involves total derivatives; solutions are univariate functions. Partial differential equation (PDE): involves partial derivatives; solutions are multivariate functions.

  36. Notation

  37. Classification

  38. Order =order of highest derivative with respect to any variable.

  39. Partial integration Instead of constant, add function of other variable(s)

  40. Partial integration

  41. Homework Section 2.10, Density stratification and the buoyancy frequency. Section 2.11, Small oscilations Section 2:12, Modes Section 3.1, Partial derivatives (typo in 4e)

  42. Application: initial condition forturbulent layer model

  43. Lake Fishing

  44. Lake Fishing Why positive and negative?

  45. Inhomogeneous fishing example

  46. Inhomogeneous fishing example Classify?

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