PHYS100
Quadrature 1
Thursday 04/09/2015
1
Terminology:
Word integration employed to describe both solutions to differential equations as
well as area under curve
Term quadrature is used to distinguish between determination of areas under
cur

PHYS100 Class Examples
Tuesday 04/07/2015
Create Chebyshev interpolants:
a) Plot resultant chenfun.
b) Determine the number of Chebyshev polynomials used.
1)
a)
tanh(10x) [-1.0, +1.0]
b)
tanh(100x

PHYS100
Lecture 14
Least Squares Solutions 01
Tuesday 03/10/2015
1
Random errors occur in almost all measurements
Repeated measurements are performed to reduce statistically contribution of
random errors
This principle taking many measurements to smooth o

PHYS100'
Lecture'13'
Roots'of'Systems'of'NonLinear'Equa;ons'
Tuesday'03/03/2015'
'
1
Material discussed in detail in (chapter/section) 6 systems_of_nonlinear_equations.pdf
6.1
Solution algorithms are extensions of algorithms for solving single nonlinear e

PHYS100
Lecture 15
Least Squares Solutions 02
Thursday 03/12/2015
1
Potential computational issues affect use of normal-equation
Consequently more robust algorithms have been developed to solve
least square problems
Techniques which preserve Euclidean

Home Work 02
PHYS100
Due: Thursday 02/26/2015
If a method is not mentioned in a problem, use whatever method you prefer.
!
!
1. Consider the problem of finding the smallest positive root of the nonlinear equation
-2x
cos(x) + 1/(1 + e ) = 0.
Solve this pr

PHYS100 Class Examples Answers
Thursday 02/05/2015
Here we are using both bisect, which we covered, and newton, which I did not cover, as examples!
NOTE for the newton method one must supply a derivative of f(x)

PHYS100
Lecture 12
4. Computational Linear Algebra 3
Summary
Thursday 02/26/2015
Solving Systems of Linear Equations (A*x = b) via LU Decomposition
Inverse
Determinant
Condition Numbers
1
Solving Arbitrary n-by-n Linear Systems
Schematic for solution, x,