Review of Power Series
An infinite series of the form
c ( x a)
n 0
Series Solutions of Linear Differential
Equations
n
n
c0 c1 ( x a ) c2 ( x a ) 2
is called a power series centered at a.
Examples:
( x 1)
2
n
n 0
n 1
xn
n 1
A power series is convergen
MANE 4240 & CIVL 4240
Introduction to Finite Elements
Prof. Suvranu De
Shape functions in 1D
Reading assignment:
Lecture notes, Logan 2.2, 3.1
Summary:
Linear shape functions in 1D
Quadratic and higher order shape functions
Approximation of strains and
Orthogonal Functions
The inner product of two functions f1 and f2 on an
interval [a , b] is the number
b
( f1 , f 2 ) f1 ( x) f 2 ( x)dx.
a
Two functions f1 and f2 are said to be orthogonal on an
interval [a , b] if
Orthogonal Functions and Fourier Series
General Definitions and Properties
If u is the dependent variable and x and y are independent variables,
the general form of a linear second-order partial differential
equations is
A
Boundary-Value Problems in
Rectangular Coordinates
2u
2u
2u
u
u
B
C