Math 227
Problems, Solutions, Handouts

Instructor
Joel Feldman
Note: PDF files may be read, for example, with
Adobe
Reader, which is available for free from Adobe. There are many
other free PDF readers available too. See this
Wikipedia page.
 Course Outline
[
html,
pdf
]

Mathematics Department Exam Database
 Tables of formulae
 Trig identities.
[ pdf ]
 Derivatives.
[ pdf ]
 Indefinite integrals.
[ pdf ]
 Properties of exponentials and logarithms.
[ pdf ]
 Taylor Expansions.
[ pdf ]
 Old Math 227 exams
 April 2013
[ questions
, answers
, solutions
]
 April 2011
[ questions
, answers
, solutions
]
 April 2009
[ questions
, answers
, solutions
]
 April 2006
[ questions
, answers
, solutions
]
 April 2005
[ questions
, answers
, solutions
]
 Final exam: Tuesday, April 19, 12:0014:30
in room BUCH B315.
 Review session: Monday, April 18, 10:0012:00 in room MATH 102.
 Exam period office hours
Tests
 Midterm 1: Wednesday, February 10, 2016
[
formula sheet included with midterm,
questions,
solutions
]
 Midterm 2: Wednesday, March 16, 2016
[
formula sheet included with midterm,
questions,
solutions
]
 Final exam: Tuesday, April 19, 12:0014:30
in room BUCH B315.
[
formula sheet included with exam ,
exam period office hours
]
Problem Sets
 Problem Set I (Due Wednesday, January 13)
[
questions
, solutions
]
 Problem Set II (Due Wednesday, January 20)
[
questions
, solutions
]
 Problem Set III (Due Wednesday, January 27)
[
questions
, solutions
]
 Problem Set IV (Due Wednesday, February 3)
[
questions
, solutions
]
 Problem Set V (Due Wednesday, February 24)
[
questions
, solutions
]
 Problem Set VI (Due Wednesday, March 2)
[
questions
, solutions
]
 Problem Set VII (Due Wednesday, March 9)
[
questions
, solutions
]
 Problem Set VIII (Due Wednesday, March 23)
[
questions
, solutions
]
 Problem Set IX (Due Friday, April 1)
[
questions
, solutions
]
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
[
version of January 15, 2016
]
 Vector Field Sketches
[
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
]
 Integration on Manifolds
[
version of April 4, 2016
]
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
]
 A Continuous Bijection with Discontinuous Inverse
[
pdf
]