Math 3003, Winter 2013
Topics: sets, functions
1
Applied Analysis - Sets and Functions
Revised: January 10, 2013
Sets and Functions
1.1
Basic notation for sets
Some good simple, open-source introductions to sets are the Wiki-Books on Set Theory1 and
Abstr
Systems of Linear Equations and Their Solutions
We have seen that all equations in the form Ax + By = C are straight lines when graphed. Two
such equations, such as those listed below, are called a system of linear equations. A solution to
a system of lin
Systems of Nonlinear Equations and Their Solutions
A system of two nonlinear equations in two variables contains at least one equation that cannot
be expressed in the form Ax + By = C. Here are two examples:
x2 = 2y + 10
3x y = 9
y = x2 + 3
x2 + y2 = 9
A
Math 3003, Winter 2013
Topics: sequences, limits and convergence
1
Applied Analysis - Sequences in R
Revised: January 10, 2013
Sequences of Real Numbers
1.1
The main denitions
Denition 1.1. A sequence is a function whose domain is the counting numbers. We
Math 3003, Winter 2013
Topics: inner products, orthogonality, projections
1
1.1
Applied Analysis - Inner Product Spaces
Revised: February 15, 2013
Inner Product Spaces
Inner products and convergence
An inner product is an abstraction of the dot product, o
Math 3003, Winter 2013
Topics: Fourier Series
8
Applied Analysis - Inner Product Spaces
Revised: March 19, 2013
Convergence of Fourier Series
We have seen that the sequence, (Tn ), of of trigonometric polynomials given by
Tn =
1
, cos(x), sin(x), cos(2x)
Math 3003, Winter 2013
Topics: vectors spaces, norms, convergence in norm
1
Applied Analysis - Norms and Convergence
Revised: February 11, 2013
Normed Linear Spaces
1.1
Vector Spaces
Typically, we think of quantities with a magnitude and direction, such a
Math 3003, Winter 2013
Applied Analysis - The Real Numbers
Topics: real numbers, open and closed sets in R, real-valued functions Revised: January 10, 2013
1
Real numbers
1.1
Length and number
Perhaps a good place to start an introduction to analysis is w
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