Math 227
Problems, Solutions, Handouts

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Notes
 Properties of Derivatives of Vector Valued Functions
[
pdf
]
 The Astroid
[
pdf,
applet
]
 Parametrizing Circles
[
pdf
]
 A Compendium of Curve Formulae
[
pdf
]
 Skateboarding in a Culvert
[
pdf
]
 Review of Ordinary Differential Equations
[
pdf
]
 The Damped Pendulum
[
pdf,
applet
]
 3d Coordinate Systems
[
pdf
]
 Flux Formulae
[
pdf
]
 Flux Integral Example
[
pdf
]
 Vector Identities
[
pdf
]
 Divergence Theorem and Variations
[
pdf
]
 Proof that "a . b x c = a x b . c"
[
pdf
]
 Buoyancy
[
pdf
]
 Stokes' Theorem
[
statement and proof
, example
]
 More About Which Vector Fields Have Curl Zero
[
pdf
]
 The Physical Significance of div and curl
[
short, simple, version ,
longer, more involved, version
]
More Notes
 Complex Numbers and Exponentials
[
pdf
]
 Hyperbolic Trig Functions
[
pdf
]
 Quadric Surfaces
[
pdf
]
 Vectors and Geometry in Two and Three Dimensions
[
pdf
]
 Precession of the Perihelion of Mercury
[
pdf,
applet
]
 Numerical Approximate Solutions to ODE's
 Simple ODE Solvers  Derivation
[ pdf ]
 Simple ODE Solvers  Error Behaviour
[ pdf ]
 Richardson Extrapolation
[ pdf ]
 The RLC Circuit
[
pdf
]
 Rigid Body Motion
 Torque
[ pdf]
 A Summary of Rigid Body Formulae
[ pdf ]
 Euler Wobble
[ pdf ]
 The Chain Rule
[
pdf
]
 The Contraction Mapping Theorem
[
pdf
]
 Circulation around a small circle
[
pdf
]
 The Divergence/Stokes' theorems and partial differential equations
[
The Heat Equation ,
Faraday's Law ,
Poisson's Equation
]
 Integration on Manifolds
[
notes ,
problem solutions
]
Transparencies used in class
 The Divergence Theorem
[
pdf
]
 The Boat
[
pdf
]
 The Paddle Wheel
[
pdf
]