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# Zen and the Art of Motorcycle Maintenance Robert Pirsig - PowerPoint PPT Presentation

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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### Zen and the Art of Motorcycle MaintenanceRobert Pirsig

• The state of “stuckness” is to be treasured. It is the moment that precedes enlightenment.

### Differential equations

REVIEW

Algebraicequation: involves functions; solutions are numbers.

Differential equation: involves derivatives; solutions are functions.

Linearity:

Homogeneity:

Order:

### Superposition(linear, homogeneous equations)

Can build a complex solution from the sum of two or more simpler solutions.

### Properties of the exponential function

Taylor series:

Sum rule:

Power rule:

Derivative

Indefinite integral

## Wednesday Sept 15th: Univariate Calculus 3

Exponential, trigonometric, hyperbolic functions

Differential eigenvalue problems

F=ma for small oscillations

### Complex numbers

The complex plane

### Oscillations

• Simple pendulum

• Waves in water

• Seismic waves

• Iceberg or buoy

• LC circuits

• Milankovich cycles

• Gyrotactic swimming

current

Swimming

direction

gravity

### Newton’s 2nd Law for Small Oscillations

=0

Small if x is small

=0

~0

=0

~0

Zero crossings

Zero crossings

Increment:

x part

y part

### Partial derivatives

Could also be changing in time:

x part

y part

t part

### 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.

### Order

=order of highest derivative with respect to any variable.

### 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)

### Lake Fishing

Why positive and negative?

Classify?