Example:
Consider the CFG
A BC|0
B BA| 1 |CC
C AB| 0
C
B
B
B
1
B
A
A
C
0
A
1
Derivation of the string
11100001
A
1
B
B
C
C
C
1
0
0
0
A BC BAC 1AC 1BCC 11CC 11ABC
11BCBC 111CBC 1110BC 1110CCC 11100CC
Pumping Lemma for Regular Languages
By: Dr.T.Sritharan
1
SCS 4008
Dr. T. Sritharan
9/20/2016
Non Regular Languages
To show that a language L is regular we can do any one of the
following:
1.
2.
3.
4.
Computability and
Decidability
By: Dr.T.Sritharan
Text Book: Languages and Machines
By: Thomas A. Sudkamp
SCS 4008
Dr. T. Sritharan
11/15/2016
Recursive & Recursively Enumerable Languages
A Language L
Topic 5:
Chomsky Normal Form
By: Dr.T.Sritharan
UCSC
1
Dr. T. Sritharan
10/3/2016
Leftmost Derivation
Let G be a
grammar
G: S AB
A AA | a
B BB | b
Consider the following derivations of aaabb
1
S AB
A
Topic 7:
Pushdown Automata
By: Dr.T.Sritharan
UCSC
1
SCS 4008
Dr. Sritharan
10/10/2016
Pushdown Automata(PDA)
Class of PDAs recognize exactly the class of Context- Free
Languages (CFLs).
Consider the
UNIVERSITY OF COLOMBO, SRI LANKA
UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING
DEGREE OF BACHELOR OF INFORMATION TECHNOLOGY (EXTERNAL)
nd
Academic Year 2010/2011 2 Year Examination Semester 3
IT3304: Math
Creating Direction Fields with DERIVE 5
Last updated: January 22, 2007 Steve Billups, modified by Lance Lana This tutorial describes how to use DERIVE 5 to generate a direction field for the first ord
Laplace Transform Table
(Adapted from Table 5.1 of Kohler and Johnson) Time Domain Function f (t), t 0 Laplace Transform F (s) a h(t) = tn , et sin(t) cos(t) sinh(t) cosh(t) et f (t), with |f (t)| M e
Math 3200 Mini-Projects
(modied from Bill Briggs 2004) This collection of assorted mini-projects is supported by the material that we will study this semester. You must complete two (2) mini-projects
Form of Particular Solution
(Adapted from Table 3.1 of Kohler and Johnson) The right-hand column gives the proper form to assume for a particular solution of ay + by + cy = g (t). In the right-hand co
MATH 3200
Review for Test 1
Bennethum
These are practice problems for test 1. For this exam, one side of an 8.5x11 sheet of paper will be allowed for notes. No technology of any kind will be allowed.
MATH 3200
Review for Test 2
Bennethum
These are practice problems for test 2. For this exam, one side of an 8.5x11 sheet of paper will be allowed for notes. No technology of any kind will be allowed.
MATH 3200 Bennethum Review Problems for Final Exam: Laplace Transforms
These are practice problems on the Laplace trasform for the nal exam. For this exam, two sides of an 8.5x11 sheet of paper will b
Review of Dierentiation and Integration for MATH 3200 UCD Department of Mathematical and Statistical Sciences
This is a packet of prerequisite material necessary for understanding material covered in
BC x
Name:
TI-89 Slope Fields, Euler, etc.
(assuming basic TI-89 knowledge) Mode Graph Diff Equations Y= F1 (9) Graph Formats Set: Solution Method Euler Fields Slpfld
To graph a slope field:
Under Y=
Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur
Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur
Chapter 2 Deformation and Strain
In this chapter we explain how deformation is described precisely. This gives us the framework to model the deformation of a metal beam for example, which is holding u
Chapter 3 Balance Laws
In this chapter we explore the governing eld equations: the conservation of mass and linear momentum, the balance of angular momentum, and the conservation of energy. Although w
Chapter 4 Introduction to Thermodynamics
In this chapter we introduce the topic of thermodynamics which are needed to develop governing equations (specically constitutive equations) for a continuous m
Chapter 5 The Entropy Inequality and Constitutive Equations
In the 1950s and 1960s, thermodynamics was combined with classical continuum mechanics to form a rational method for developing constitutive
Chapter 6 Miscellaneous Topics
6.1 Boundary Conditions
After determining the governing equations one must determine appropriate boundary and initial conditions which make the problem physically meanin
Project Information
Continuum Mechanics, Spring 2008 Due 4pm, Friday May 9, 2008 The project for this course consists of two parts: the written report and the oral report. The written report (worth 80