Solving Recursive Sequences by Iteration
|
|
- Gervase Summers
- 6 years ago
- Views:
Transcription
1 Solving Recursive Sequences by Iteration Lecture 25 Section 5.7 Robb T. Koether Hampden-Sydney College Thu, Feb 28, 2013 Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
2 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
3 Outline 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
4 Outline 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
5 The Towers of Hanoi In the Towers of Hanoi problem, we found the recursive sequence to be m 1 = 1 and m n = 2m n We used it to calculate the first few terms: 1, 3, 7, 15. A nonrecursive formula for m n would allow us to calculate m n directly for an n. How do we find a nonrecursive formula for m n? Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
6 The Towers of Hanoi The method of iteration is to apply the recursive formula repeatedly, but postpone most of the calculations, until we see a pattern develop. m 1 = 1. m 2 = m 3 = 2(2 + 1) + 1 = m 4 = 2( ) + 1 = Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
7 The Towers of Hanoi The pattern is clear: m n = 2 n n This is a sum of a geometric series, for which the formula n k=0 r k = r n+1 1 r 1 applies. Thus, m n = 2n = 2 n 1. Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
8 Outline 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
9 Example Define a sequence {a n } by a 0 = 1, a n = 5a n 1 2, for all n 1. Use the method of iteration to find a nonrecursive formula. Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
10 Example Write expressions for the first few terms, until a clear pattern develops. a 0 = 1. a 1 = 5 2. a 2 = 5(5 2) 2 = a 3 = 5( ) 2 = a 4 = 5( ) 2 = Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
11 Example Again, the pattern is clear: ( ) a n = 5 n 2 5 n ( 5 = 5 n n ) = 5 n 5n 1 2 = 1 2 (5n + 1). Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
12 Outline 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
13 Annuities An annuity is a sum of money from which we can draw over a period of time. Suppose the sum is earning 4% interest annually and a person deposits $5,000 annually for 40 years. How much will he have at retirement? Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
14 Annuities Let A n be the amount in the account after n years. If we deposit $5,000 at the end of each year, then A 0 = 0 and A 1 = At the end of each subsequent year, we earn 4% interest on the balance and then deposit another $5,000. The recursive formula is A n = 0.04A n Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
15 Annuities We calculate A 2 = = 5000 ( ). A 3 = ( ) ( ) = ( ) A 4 = ( ) = Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
16 Annuities Clearly, So, ( ) A n = n ( 1.04 n ) 1 A n = ( 1.04 n ) 1 = Generalize this to an interest rate of r, a deposit of P, and a period of n years. Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
17 Annuities Given that the person has accumulated A dollars in his annuity, how much can he withdraw each year for m years of retirement if the balance continues to earn an interest rate of r? Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
18 Outline 1 Solving Recursive Relations by Iteration The Towers of Hanoi Another Example Annuities 2 Assignment Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
19 Assignment Assignment Read Section 5.7, pages Exercises 2, 5, 7, 22, 23, 25, 26, 27, 52, page 314. Robb T. Koether (Hampden-Sydney College) Solving Recursive Sequences by Iteration Thu, Feb 28, / 19
Recursive Sequences. Lecture 24 Section 5.6. Robb T. Koether. Hampden-Sydney College. Wed, Feb 26, 2014
Recursive Sequences Lecture 24 Section 5.6 Robb T. Koether Hampden-Sydney College Wed, Feb 26, 2014 Robb T. Koether (Hampden-Sydney College) Recursive Sequences Wed, Feb 26, 2014 1 / 26 1 Recursive Sequences
More informationRecursive Sequences. Lecture 24 Section 5.6. Robb T. Koether. Hampden-Sydney College. Wed, Feb 27, 2013
Recursive Sequences Lecture 24 Section 5.6 Robb T. Koether Hampden-Sydney College Wed, Feb 27, 2013 Robb T. Koether (Hampden-Sydney College) Recursive Sequences Wed, Feb 27, 2013 1 / 21 1 Recursive Sequences
More informationMinimal Spanning Trees
Minimal Spanning Trees Lecture 33 Sections 7.1-7.3 Robb T. Koether Hampden-Sydney College Wed, Apr 11, 20 Robb T. Koether (Hampden-Sydney College) Minimal Spanning Trees Wed, Apr 11, 20 1 / 17 1 Networks
More informationThe Critical-Path Algorithm
The Critical-Path Algorithm Lecture 32 Sections 8.3-8.4 Robb T. Koether Hampden-Sydney College Wed, Nov 19, 2014 Robb T. Koether (Hampden-Sydney College) The Critical-Path Algorithm Wed, Nov 19, 2014 1
More informationThe Traveling Salesman Problem Brute Force Method
The Traveling Salesman Problem Brute Force Method Lecture 30 Sections 6.1, 6.3 Robb T. Koether Hampden-Sydney College Fri, Nov 3, 2017 Robb T. Koether (Hampden-Sydney College)The Traveling Salesman Problem
More informationScheduling and Digraphs
Scheduling and Digraphs Lecture 35 Sections 8.1, 8.2 Robb T. Koether Hampden-Sydney College Mon, Nov 21, 2016 Robb T. Koether (Hampden-Sydney College) Scheduling and Digraphs Mon, Nov 21, 2016 1 / 25 1
More informationThe Pairwise-Comparison Method
The Pairwise-Comparison Method Lecture 10 Section 1.5 Robb T. Koether Hampden-Sydney College Mon, Sep 11, 2017 Robb T. Koether (Hampden-Sydney College) The Pairwise-Comparison Method Mon, Sep 11, 2017
More informationwhile Loops Lecture 13 Sections Robb T. Koether Wed, Sep 26, 2018 Hampden-Sydney College
while Loops Lecture 13 Sections 5.8-5.9 Robb T. Koether Hampden-Sydney College Wed, Sep 26, 2018 Robb T. Koether (Hampden-Sydney College) while Loops Wed, Sep 26, 2018 1 / 25 1 while Loops 2 Input Loops
More informationRotations and Translations
Rotations and Translations Lecture 33 Sections 11.3-11.4 Robb T. Koether Hampden-Sydney College Wed, Nov 20, 2013 Robb T. Koether (Hampden-Sydney College) Rotations and Translations Wed, Nov 20, 2013 1
More informationThe Decreasing-Time Algorithm
The Decreasing-Time Algorithm Lecture 36 Sections 8.4 Robb T. Koether Hampden-Sydney College Wed, Apr 18, 2018 Robb T. Koether (Hampden-Sydney College) The Decreasing-Time Algorithm Wed, Apr 18, 2018 1
More informationThe Traveling Salesman Problem Nearest-Neighbor Algorithm
The Traveling Salesman Problem Nearest-Neighbor Algorithm Lecture 31 Sections 6.4 Robb T. Koether Hampden-Sydney College Fri, Apr 6, 2018 Robb T. Koether (Hampden-Sydney College)The Traveling Salesman
More informationThe Plurality-with-Elimination Method
The Plurality-with-Elimination Method Lecture 9 Section 1.4 Robb T. Koether Hampden-Sydney College Fri, Sep 8, 2017 Robb T. Koether (Hampden-Sydney College) The Plurality-with-Elimination Method Fri, Sep
More informationLR Parsing - Conflicts
LR Parsing - Conflicts Lecture 15 Sections 4.5, 4.6 Robb T. Koether Hampden-Sydney College Fri, Feb 20, 2015 Robb T. Koether (Hampden-Sydney College) LR Parsing - Conflicts Fri, Feb 20, 2015 1 / 15 1 Shift/Reduce
More informationSampling Distribution Examples Sections 15.4, 15.5
Sampling Distribution Examples Sections 15.4, 15.5 Lecture 27 Robb T. Koether Hampden-Sydney College Wed, Mar 2, 2016 Robb T. Koether (Hampden-Sydney College)Sampling Distribution ExamplesSections 15.4,
More informationBoxplots. Lecture 17 Section Robb T. Koether. Hampden-Sydney College. Wed, Feb 10, 2010
Boxplots Lecture 17 Section 5.3.3 Robb T. Koether Hampden-Sydney College Wed, Feb 10, 2010 Robb T. Koether (Hampden-Sydney College) Boxplots Wed, Feb 10, 2010 1 / 34 Outline 1 Boxplots TI-83 Boxplots 2
More informationScope and Parameter Passing
Scope and Parameter Passing Lecture 16 Sections 6.5, 6.10, 6.13 Robb T. Koether Hampden-Sydney College Mon, Oct 7, 2013 Robb T. Koether (Hampden-Sydney College) Scope and Parameter Passing Mon, Oct 7,
More informationRecursion. Lecture 2 Sections Robb T. Koether. Hampden-Sydney College. Wed, Jan 17, 2018
Recursion Lecture 2 Sections 20.1-20.4 Robb T. Koether Hampden-Sydney College Wed, Jan 17, 2018 Robb T. Koether (Hampden-Sydney College) Recursion Wed, Jan 17, 2018 1 / 18 1 Recursion 2 Advantages and
More informationBinary Tree Applications
Binary Tree Applications Lecture 30 Section 19.2 Robb T. Koether Hampden-Sydney College Wed, Apr 15, 2015 Robb T. Koether (Hampden-Sydney College) Binary Tree Applications Wed, Apr 15, 2015 1 / 56 1 Binary
More informationRecursive Linked Lists
Recursive Linked Lists Lecture 28 Sections 14.1-14.5, 14.7 Robb T. Koether Hampden-Sydney College Fri, Mar 31, 2017 Robb T. Koether (Hampden-Sydney College) Recursive Linked Lists Fri, Mar 31, 2017 1 /
More informationTotal Orders. Lecture 41 Section 8.5. Robb T. Koether. Hampden-Sydney College. Mon, Apr 8, 2013
Total Orders Lecture 41 Section 8.5 Robb T. Koether Hampden-Sydney College Mon, Apr 8, 2013 Robb T. Koether (Hampden-Sydney College) Total Orders Mon, Apr 8, 2013 1 / 30 1 Total Orders 2 Topological Sorting
More informationRecursive Descent Parsers
Recursive Descent Parsers Lecture 7 Robb T. Koether Hampden-Sydney College Wed, Jan 28, 2015 Robb T. Koether (Hampden-Sydney College) Recursive Descent Parsers Wed, Jan 28, 2015 1 / 18 1 Parsing 2 LL Parsers
More informationStreet-Routing Problems
Street-Routing Problems Lecture 26 Sections 5.1-5.2 Robb T. Koether Hampden-Sydney College Wed, Oct 25, 2017 Robb T. Koether (Hampden-Sydney College) Street-Routing Problems Wed, Oct 25, 2017 1 / 21 1
More informationDisplaying Distributions - Quantitative Variables
Displaying Distributions - Quantitative Variables Lecture 13 Sections 4.4.1-4.4.3 Robb T. Koether Hampden-Sydney College Wed, Feb 8, 2012 Robb T. Koether (Hampden-Sydney College)Displaying Distributions
More informationScope and Parameter Passing
Scope and Parameter Passing Lecture 17 Sections 6.5, 6.10, 6.13 Robb T. Koether Hampden-Sydney College Fri, Oct 5, 2018 Robb T. Koether (Hampden-Sydney College) Scope and Parameter Passing Fri, Oct 5,
More informationThe Coefficient of Determination
The Coefficient of Determination Lecture 46 Section 13.9 Robb T. Koether Hampden-Sydney College Wed, Apr 17, 2012 Robb T. Koether (Hampden-Sydney College) The Coefficient of Determination Wed, Apr 17,
More informationStack Applications. Lecture 27 Sections Robb T. Koether. Hampden-Sydney College. Wed, Mar 29, 2017
Stack Applications Lecture 27 Sections 18.7-18.8 Robb T. Koether Hampden-Sydney College Wed, Mar 29, 2017 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, 2017 1 / 27 1 Function
More informationRecursion. Lecture 26 Sections , Robb T. Koether. Hampden-Sydney College. Mon, Apr 6, 2015
Recursion Lecture 26 Sections 14.1-14.5, 14.7 Robb T. Koether Hampden-Sydney College Mon, Apr 6, 2015 Robb T. Koether (Hampden-Sydney College) Recursion Mon, Apr 6, 2015 1 / 18 1 Recursion 2 Advantages
More informationDensity Curves Sections
Density Curves Sections 3.1-3.2 Lecture 8 Robb T. Koether Hampden-Sydney College Wed, Jan 27, 2016 Robb T. Koether (Hampden-Sydney College) Density CurvesSections 3.1-3.2 Wed, Jan 27, 2016 1 / 18 Outline
More informationImplementing Linked Lists
Implementing Linked Lists Lecture 16 Sections 17.1-17.3 Robb T. Koether Hampden-Sydney College Wed, Feb 27, 2013 Robb T. Koether (Hampden-Sydney College) Implementing Linked Lists Wed, Feb 27, 2013 1 /
More informationXPath Lecture 34. Robb T. Koether. Hampden-Sydney College. Wed, Apr 11, 2012
XPath Lecture 34 Robb T. Koether Hampden-Sydney College Wed, Apr 11, 2012 Robb T. Koether (Hampden-Sydney College) XPathLecture 34 Wed, Apr 11, 2012 1 / 20 1 XPath Functions 2 Predicates 3 Axes Robb T.
More informationBoolean Expressions. Lecture 31 Sections 6.6, 6.7. Robb T. Koether. Hampden-Sydney College. Wed, Apr 8, 2015
Boolean Expressions Lecture 31 Sections 6.6, 6.7 Robb T. Koether Hampden-Sydney College Wed, Apr 8, 2015 Robb T. Koether (Hampden-Sydney College) Boolean Expressions Wed, Apr 8, 2015 1 / 22 1 Relational
More informationOperators. Lecture 12 Section Robb T. Koether. Hampden-Sydney College. Fri, Feb 9, 2018
Operators Lecture 12 Section 14.5 Robb T. Koether Hampden-Sydney College Fri, Feb 9, 2018 Robb T. Koether (Hampden-Sydney College) Operators Fri, Feb 9, 2018 1 / 21 Outline 1 Operators as Functions 2 Operator
More informationThe Class Construct Part 1
The Class Construct Part 1 Lecture 23 Sections 7.5-7.6 Robb T. Koether Hampden-Sydney College Fri, Oct 26, 2018 Robb T. Koether (Hampden-Sydney College) The Class Construct Part 1 Fri, Oct 26, 2018 1 /
More informationFriends and Unary Operators
Friends and Unary Operators Lecture 11 Sections 11.3, 11.6 Robb T. Koether Hampden-Sydney College Fri, Feb 13, 2015 Robb T. Koether (Hampden-Sydney College) Friends and Unary Operators Fri, Feb 13, 2015
More informationMagnification and Minification
Magnification and Minification Lecture 30 Robb T. Koether Hampden-Sydney College Fri, Nov 6, 2015 Robb T. Koether (Hampden-Sydney College) Magnification and Minification Fri, Nov 6, 2015 1 / 17 Outline
More informationRecognition of Tokens
Recognition of Tokens Lecture 3 Section 3.4 Robb T. Koether Hampden-Sydney College Mon, Jan 19, 2015 Robb T. Koether (Hampden-Sydney College) Recognition of Tokens Mon, Jan 19, 2015 1 / 21 1 A Class of
More informationLinked Lists. Lecture 16 Sections Robb T. Koether. Hampden-Sydney College. Wed, Feb 22, 2017
Linked Lists Lecture 16 Sections 17.1-17.3 Robb T. Koether Hampden-Sydney College Wed, Feb 22, 2017 Robb T. Koether (Hampden-Sydney College) Linked Lists Wed, Feb 22, 2017 1 / 24 1 Linked Lists 2 The LinkedListNode
More informationLR Parsing - The Items
LR Parsing - The Items Lecture 10 Sections 4.5, 4.7 Robb T. Koether Hampden-Sydney College Fri, Feb 13, 2015 Robb T. Koether (Hampden-Sydney College) LR Parsing - The Items Fri, Feb 13, 2015 1 / 31 1 LR
More informationPHP Queries and HTML Forms Lecture 23
PHP Queries and HTML Forms Lecture 23 Robb T. Koether Hampden-Sydney College Wed, Mar 14, 2018 Robb T. Koether (Hampden-Sydney College) PHP Queries and HTML FormsLecture 23 Wed, Mar 14, 2018 1 / 15 1 Retrieving
More informationRegular Expressions. Lecture 10 Sections Robb T. Koether. Hampden-Sydney College. Wed, Sep 14, 2016
Regular Expressions Lecture 10 Sections 3.1-3.2 Robb T. Koether Hampden-Sydney College Wed, Sep 14, 2016 Robb T. Koether (Hampden-Sydney College) Regular Expressions Wed, Sep 14, 2016 1 / 23 Outline 1
More informationAbstract Data Types. Lecture 23 Section 7.1. Robb T. Koether. Hampden-Sydney College. Wed, Oct 24, 2012
Abstract Data Types Lecture 23 Section 7.1 Robb T. Koether Hampden-Sydney College Wed, Oct 24, 2012 Robb T. Koether (Hampden-Sydney College) Abstract Data Types Wed, Oct 24, 2012 1 / 19 1 Abstract Data
More informationXQuery FLOWR Expressions Lecture 35
XQuery FLOWR Expressions Lecture 35 Robb T. Koether Hampden-Sydney College Fri, Apr 13, 2012 Robb T. Koether (Hampden-Sydney College) XQuery FLOWR ExpressionsLecture 35 Fri, Apr 13, 2012 1 / 33 1 XQuery
More informationXPath. Lecture 36. Robb T. Koether. Wed, Apr 16, Hampden-Sydney College. Robb T. Koether (Hampden-Sydney College) XPath Wed, Apr 16, / 28
XPath Lecture 36 Robb T. Koether Hampden-Sydney College Wed, Apr 16, 2014 Robb T. Koether (Hampden-Sydney College) XPath Wed, Apr 16, 2014 1 / 28 1 XPath 2 Executing XPath Expressions 3 XPath Expressions
More informationArray Lists. Lecture 15. Robb T. Koether. Hampden-Sydney College. Fri, Feb 16, 2018
Array Lists Lecture 15 Robb T. Koether Hampden-Sydney College Fri, Feb 16, 2018 Robb T. Koether (Hampden-Sydney College) Array Lists Fri, Feb 16, 2018 1 / 21 1 Inlining Functions 2 List Implementations
More informationThe Graphics Pipeline
The Graphics Pipeline Lecture 2 Robb T. Koether Hampden-Sydney College Fri, Aug 28, 2015 Robb T. Koether (Hampden-Sydney College) The Graphics Pipeline Fri, Aug 28, 2015 1 / 19 Outline 1 Vertices 2 The
More informationBinary Tree Implementation
Binary Tree Implementation Lecture 32 Section 19.1 Robb T. Koether Hampden-Sydney College Mon, Apr 16, 2018 Robb T. Koether (Hampden-Sydney College) Binary Tree Implementation Mon, Apr 16, 2018 1 / 24
More informationList Iterator Implementation
List Iterator Implementation Lecture 28 Section 14.6 Robb T. Koether Hampden-Sydney College Fri, Apr 10, 2015 Robb T. Koether (Hampden-Sydney College) List Iterator Implementation Fri, Apr 10, 2015 1 /
More informationThe Graphics Pipeline
The Graphics Pipeline Lecture 2 Robb T. Koether Hampden-Sydney College Wed, Aug 23, 2017 Robb T. Koether (Hampden-Sydney College) The Graphics Pipeline Wed, Aug 23, 2017 1 / 19 Outline 1 Vertices 2 The
More informationInteger Overflow. Lecture 8 Section 2.5. Robb T. Koether. Hampden-Sydney College. Mon, Jan 27, 2014
Integer Overflow Lecture 8 Section 2.5 Robb T. Koether Hampden-Sydney College Mon, Jan 27, 2014 Robb T. Koether (Hampden-Sydney College) Integer Overflow Mon, Jan 27, 2014 1 / 32 1 Signed Addition and
More informationNondeterministic Programming in C++
Nondeterministic Programming in C++ Lecture 37 Sections 14.5 Robb T. Koether Hampden-Sydney College Wed, Nov 30, 2016 Robb T. Koether (Hampden-Sydney College) Nondeterministic Programming in C++ Wed, Nov
More informationTriggers. Lecture 14. Robb T. Koether. Hampden-Sydney College. Wed, Feb 14, 2018
Triggers Lecture 14 Robb T. Koether Hampden-Sydney College Wed, Feb 14, 2018 Robb T. Koether (Hampden-Sydney College) Triggers Wed, Feb 14, 2018 1 / 22 1 Triggers 2 Cascading Triggers 3 Update and Insert
More informationMipmaps. Lecture 35. Robb T. Koether. Hampden-Sydney College. Wed, Nov 18, 2015
Mipmaps Lecture 35 Robb T. Koether Hampden-Sydney College Wed, Nov 18, 2015 Robb T. Koether (Hampden-Sydney College) Mipmaps Wed, Nov 18, 2015 1 / 31 Outline 1 Discrete Sampling 2 Mipmaps 3 Generating
More informationAggregation. Lecture 7 Section Robb T. Koether. Hampden-Sydney College. Wed, Jan 29, 2014
Aggregation Lecture 7 Section 5.1.7-5.1.8 Robb T. Koether Hampden-Sydney College Wed, Jan 29, 2014 Robb T. Koether (Hampden-Sydney College) Aggregation Wed, Jan 29, 2014 1 / 17 1 Aggregate Functions 2
More informationThe string Class. Lecture 21 Sections 2.9, 3.9, Robb T. Koether. Wed, Oct 17, Hampden-Sydney College
The string Class Lecture 21 Sections 2.9, 3.9, 3.10 Robb T. Koether Hampden-Sydney College Wed, Oct 17, 2018 Robb T. Koether (Hampden-Sydney College) The string Class Wed, Oct 17, 2018 1 / 18 1 The String
More informationWebpage Navigation. Lecture 27. Robb T. Koether. Hampden-Sydney College. Mon, Apr 2, 2018
Webpage Navigation Lecture 27 Robb T. Koether Hampden-Sydney College Mon, Apr 2, 2018 Robb T. Koether (Hampden-Sydney College) Webpage Navigation Mon, Apr 2, 2018 1 / 16 1 Popup Boxes 2 The Document Object
More informationThe CYK Parsing Algorithm
The CYK Parsing Algorithm Lecture 19 Section 6.3 Robb T. Koether Hampden-Sydney College Fri, Oct 7, 2016 Robb T. Koether (Hampden-Sydney College) The CYK Parsing Algorithm Fri, Oct 7, 2016 1 / 21 1 The
More informationProgramming Languages
Programming Languages Lecture 3 Section 1.3 Robb T. Koether Hampden-Sydney College Mon, Sep 2, 2013 Robb T. Koether (Hampden-Sydney College) Programming Languages Mon, Sep 2, 2013 1 / 25 1 Programming
More informationIntroduction to Databases
Introduction to Databases Lecture 1 Chapters 1-2 Robb T. Koether Hampden-Sydney College Wed, Jan 15, 2014 Robb T. Koether (Hampden-Sydney College) Introduction to Databases Wed, Jan 15, 2014 1 / 23 1 Overview
More informationProgramming Languages
Programming Languages Lecture 3 Robb T. Koether Hampden-Sydney College Fri, Aug 31, 2018 Robb T. Koether (Hampden-Sydney College) Programming Languages Fri, Aug 31, 2018 1 / 23 1 Programming Languages
More informationArray Lists. Lecture 15. Robb T. Koether. Hampden-Sydney College. Mon, Feb 22, 2016
Array Lists Lecture 15 Robb T. Koether Hampden-Sydney College Mon, Feb 22, 2016 Robb T. Koether (Hampden-Sydney College) Array Lists Mon, Feb 22, 2016 1 / 23 1 Inlining Functions 2 List Implementations
More informationThe Normal Distribution
The Normal Distribution Lecture 20 Section 6.3.1 Robb T. Koether Hampden-Sydney College Wed, Sep 28, 2011 Robb T. Koether (Hampden-Sydney College) The Normal Distribution Wed, Sep 28, 2011 1 / 41 Outline
More informationStack Applications. Lecture 25 Sections Robb T. Koether. Hampden-Sydney College. Mon, Mar 30, 2015
Stack Applications Lecture 25 Sections 18.7-18.8 Robb T. Koether Hampden-Sydney College Mon, Mar 30, 2015 Robb T. Koether Hampden-Sydney College) Stack Applications Mon, Mar 30, 2015 1 / 34 1 The Triangle
More informationThe Projection Matrix
The Projection Matrix Lecture 8 Robb T. Koether Hampden-Sydney College Fri, Sep 11, 2015 Robb T. Koether (Hampden-Sydney College) The Projection Matrix Fri, Sep 11, 2015 1 / 43 Outline 1 Coordinate Systems
More informationBuilding the Abstract Syntax Trees
Building the Abstract Syntax Trees Lecture 23 Section 5.3 Robb T. Koether Hampden-Sydney College Wed, Mar 18, 2015 Robb T. Koether (Hampden-Sydney College) Building the Abstract Syntax Trees Wed, Mar 18,
More informationXML Attributes. Lecture 33. Robb T. Koether. Hampden-Sydney College. Wed, Apr 25, 2018
XML Attributes Lecture 33 Robb T. Koether Hampden-Sydney College Wed, Apr 25, 2018 Robb T. Koether (Hampden-Sydney College) XML Attributes Wed, Apr 25, 2018 1 / 15 1 XML Attributes 2 The getattribute()
More informationPointers. Lecture 1 Sections Robb T. Koether. Hampden-Sydney College. Wed, Jan 14, 2015
Pointers Lecture 1 Sections 10.1-10.2 Robb T. Koether Hampden-Sydney College Wed, Jan 14, 2015 Robb T. Koether (Hampden-Sydney College) Pointers Wed, Jan 14, 2015 1 / 23 1 Pointers 2 Pointer Initialization
More informationPointers. Lecture 2 Sections Robb T. Koether. Hampden-Sydney College. Fri, Jan 18, 2013
Pointers Lecture 2 Sections 10.3-10.8 Robb T. Koether Hampden-Sydney College Fri, Jan 18, 2013 Robb T. Koether (Hampden-Sydney College) Pointers Fri, Jan 18, 2013 1 / 35 1 Introduction 2 Pointer Arithmetic
More informationPointer Arithmetic. Lecture 4 Chapter 10. Robb T. Koether. Hampden-Sydney College. Wed, Jan 25, 2017
Pointer Arithmetic Lecture 4 Chapter 10 Robb T. Koether Hampden-Sydney College Wed, Jan 25, 2017 Robb T. Koether (Hampden-Sydney College) Pointer Arithmetic Wed, Jan 25, 2017 1 / 36 1 Pointer Arithmetic
More informationPointers. Lecture 2 Sections Robb T. Koether. Hampden-Sydney College. Mon, Jan 20, 2014
Pointers Lecture 2 Sections 10.3-10.8 Robb T. Koether Hampden-Sydney College Mon, Jan 20, 2014 Robb T. Koether (Hampden-Sydney College) Pointers Mon, Jan 20, 2014 1 / 35 1 Endianness 2 Pointer Arithmetic
More informationBasic PHP. Lecture 19. Robb T. Koether. Hampden-Sydney College. Mon, Feb 26, 2108
Basic PHP Lecture 19 Robb T. Koether Hampden-Sydney College Mon, Feb 26, 2108 Robb T. Koether (Hampden-Sydney College) Basic PHP Mon, Feb 26, 2108 1 / 27 1 PHP 2 The echo Statement 3 Variables 4 Operators
More informationIntroduction to Databases
Introduction to Databases Lecture 1 Robb T. Koether Hampden-Sydney College Mon, Jan 15, 2018 Robb T. Koether (Hampden-Sydney College) Introduction to Databases Mon, Jan 15, 2018 1 / 16 1 Overview of the
More informationBinary Tree Implementation
Binary Tree Implementation Lecture 31 Sections 12.2-12.3 Robb T. Koether Hampden-Sydney College Mon, Apr 5, 2010 Robb T. Koether (Hampden-Sydney College) Binary Tree Implementation Mon, Apr 5, 2010 1 /
More informationAmbient and Diffuse Light
Ambient and Diffuse Light Lecture 20 Robb T. Koether Hampden-Sydney College Mon, Oct 12, 2015 Robb T. Koether (Hampden-Sydney College) Ambient and Diffuse Light Mon, Oct 12, 2015 1 / 29 Outline 1 Lighting
More informationRelational Databases Lecture 2
Relational Databases Lecture 2 Robb T Koether Hampden-Sydney College Fri, Jan 20, 2012 Robb T Koether (Hampden-Sydney College) Relational DatabasesLecture 2 Fri, Jan 20, 2012 1 / 36 1 Databases Systems
More informationFunction Definition Syntax Tree
Function Definition Syntax Tree Lecture 34 Section 6.9 Robb T. Koether Hampden-Sydney College Wed, Apr 15, 2015 Robb T. Koether (Hampden-Sydney College) Function Definition Syntax Tree Wed, Apr 15, 2015
More informationThe Projection Matrix
The Projection Matrix Lecture 5 Robb T. Koether Hampden-Sydney College Wed, Aug 30, 2017 Robb T. Koether (Hampden-Sydney College) The Projection Matrix Wed, Aug 30, 2017 1 / 21 Outline 1 The World Coordinate
More informationSpecular Reflection. Lecture 19. Robb T. Koether. Hampden-Sydney College. Wed, Oct 4, 2017
Specular Reflection Lecture 19 Robb T. Koether Hampden-Sydney College Wed, Oct 4, 2017 Robb T. Koether (Hampden-Sydney College) Specular Reflection Wed, Oct 4, 2017 1 / 22 Outline 1 Specular Reflection
More informationThe Model Stack. Lecture 8. Robb T. Koether. Hampden-Sydney College. Wed, Sep 6, 2017
The Model Stack Lecture 8 Robb T. Koether Hampden-Sydney College Wed, Sep 6, 2017 Robb T. Koether (Hampden-Sydney College) The Model Stack Wed, Sep 6, 2017 1 / 19 Outline 1 Drawing Rectangle Man 2 The
More informationInheritance: The Fundamental Functions
Inheritance: The Fundamental Functions Lecture 21 Sections 11.11-11.12 Robb T. Koether Hampden-Sydney College Wed, Mar 20, 2013 Robb T. Koether (Hampden-Sydney College) Inheritance: The Fundamental Functions
More informationThe Constructors. Lecture 7 Sections Robb T. Koether. Hampden-Sydney College. Wed, Feb 1, 2017
The Constructors Lecture 7 Sections 11.4-11.5 Robb T. Koether Hampden-Sydney College Wed, Feb 1, 2017 Robb T. Koether (Hampden-Sydney College) The Constructors Wed, Feb 1, 2017 1 / 25 1 The Four Fundamental
More informationList Iterators. Lecture 27 Section Robb T. Koether. Hampden-Sydney College. Wed, Apr 8, 2015
List Iterators Lecture 27 Section 16.5 Robb T. Koether Hampden-Sydney College Wed, Apr 8, 2015 Robb T. Koether (Hampden-Sydney College) List Iterators Wed, Apr 8, 2015 1 / 28 1 Sequential Access 2 List
More informationThe Mesh Class. Lecture 26. Robb T. Koether. Wed, Oct 28, Hampden-Sydney College
The Mesh Class Lecture 26 Robb T. Koether Hampden-Sydney College Wed, Oct 28, 2015 Robb T. Koether (Hampden-Sydney College) The Mesh Class Wed, Oct 28, 2015 1 / 23 Outline 1 The Mesh Class 2 Assignment
More informationInheritance: The Fundamental Functions
Inheritance: The Fundamental Functions Lecture 21 Sections 11.11-11.12 Robb T. Koether Hampden-Sydney College Mon, Mar 17, 2014 Robb T. Koether (Hampden-Sydney College) Inheritance: The Fundamental Functions
More informationBasic PHP Lecture 17
Basic PHP Lecture 17 Robb T. Koether Hampden-Sydney College Fri, Feb 24, 2012 Robb T. Koether (Hampden-Sydney College) Basic PHPLecture 17 Fri, Feb 24, 2012 1 / 30 1 PHP 2 Basic PHP 3 The Extended echo
More informationMySQL Creating a Database Lecture 3
MySQL Creating a Database Lecture 3 Robb T Koether Hampden-Sydney College Mon, Jan 23, 2012 Robb T Koether (Hampden-Sydney College) MySQL Creating a DatabaseLecture 3 Mon, Jan 23, 2012 1 / 31 1 Multiple
More informationFunction Usage. Lecture 15 Sections 6.3, 6.4. Robb T. Koether. Hampden-Sydney College. Mon, Oct 1, 2018
Function Usage Lecture 15 Sections 6.3, 6.4 Robb T. Koether Hampden-Sydney College Mon, Oct 1, 2018 Robb T. Koether (Hampden-Sydney College) Function Usage Mon, Oct 1, 2018 1 / 12 1 Function and Parameters
More informationFunctional Dependencies and Normal Forms
Functional Dependencies and Normal Forms Lecture 9 Sections 15.1-15.4 Robb T. Koether Hampden-Sydney College Mon, Feb 4, 2013 Robb T. Koether (Hampden-Sydney College) Functional Dependencies and Normal
More informationFunctional Dependencies and Normal Forms
Functional Dependencies and Normal Forms Lecture 9 Sections 15.1-15.4 Robb T. Koether Hampden-Sydney College Mon, Feb 3, 2014 Robb T. Koether (Hampden-Sydney College) Functional Dependencies and Normal
More informationList Iterators. Lecture 34 Section Robb T. Koether. Hampden-Sydney College. Wed, Apr 24, 2013
List Iterators Lecture 34 Section 16.5 Robb T. Koether Hampden-Sydney College Wed, Apr 24, 2013 Robb T. Koether (Hampden-Sydney College) List Iterators Wed, Apr 24, 2013 1 / 29 1 Sequential Access 2 List
More informationReview. Lecture 39. Robb T. Koether. Mon, Dec 5, Hampden-Sydney College. Robb T. Koether (Hampden-Sydney College) Review Mon, Dec 5, / 14
Review Lecture 39 Robb T. Koether Hampden-Sydney College Mon, Dec 5, 2016 Robb T. Koether (Hampden-Sydney College) Review Mon, Dec 5, 2016 1 / 14 1 The Exam Test #2 Test #3 Robb T. Koether (Hampden-Sydney
More informationThe x86 Instruction Set
The x86 Instruction Set Lecture 25 Intel Manual, Vols. 2A & 2B Robb T. Koether Hampden-Sydney College Mon, Mar 23, 2015 Robb T. Koether (Hampden-Sydney College) The x86 Instruction Set Mon, Mar 23, 2015
More informationDTDs and XML Attributes
DTDs and XML Attributes Lecture 33 Robb T. Koether Hampden-Sydney College Mon, Apr 8, 2013 Robb T. Koether (Hampden-Sydney College) DTDs and XML Attributes Mon, Apr 8, 2013 1 / 21 1 Attribute Definitions
More informationIntroduction to Compiler Design
Introduction to Compiler Design Lecture 1 Chapters 1 and 2 Robb T. Koether Hampden-Sydney College Wed, Jan 14, 2015 Robb T. Koether (Hampden-Sydney College) Introduction to Compiler Design Wed, Jan 14,
More informationRelational Databases
Relational Databases Lecture 2 Chapter 3 Robb T. Koether Hampden-Sydney College Fri, Jan 18, 2013 Robb T. Koether (Hampden-Sydney College) Relational Databases Fri, Jan 18, 2013 1 / 26 1 Types of Databases
More informationForm Validation. Lecture 25. Robb T. Koether. Hampden-Sydney College. Wed, Mar 23, 2018
Form Validation Lecture 25 Robb T. Koether Hampden-Sydney College Wed, Mar 23, 2018 Robb T. Koether (Hampden-Sydney College) Form Validation Wed, Mar 23, 2018 1 / 16 1 Form Validation 2 Detecting Javascript
More informationCUP. Lecture 18 CUP User s Manual (online) Robb T. Koether. Hampden-Sydney College. Fri, Feb 27, 2015
CUP Lecture 18 CUP User s Manual (online) Robb T. Koether Hampden-Sydney College Fri, Feb 27, 2015 Robb T. Koether (Hampden-Sydney College) CUP Fri, Feb 27, 2015 1 / 31 1 The CUP Parser Generator 2 The
More informationStacks and their Applications
Stacks and their Applications Lecture 23 Sections 18.1-18.2 Robb T. Koether Hampden-Sydney College Fri, Mar 16, 2018 Robb T. Koether Hampden-Sydney College) Stacks and their Applications Fri, Mar 16, 2018
More informationShading Triangles. Lecture 37. Robb T. Koether. Hampden-Sydney College. Mon, Nov 30, 2015
Shading Triangles Lecture 37 Robb T. Koether Hampden-Sydney College Mon, Nov 30, 2015 Robb T. Koether (Hampden-Sydney College) Shading Triangles Mon, Nov 30, 2015 1 / 35 Outline 1 Shading Triangles Barycentric
More informationThe x86 Architecture
The x86 Architecture Lecture 24 Intel Manual, Vol. 1, Chapter 3 Robb T. Koether Hampden-Sydney College Fri, Mar 20, 2015 Robb T. Koether (Hampden-Sydney College) The x86 Architecture Fri, Mar 20, 2015
More informationBasic CSS Lecture 17
Basic CSS Lecture 17 Robb T. Koether Hampden-Sydney College Wed, Feb 21, 2018 Robb T. Koether (Hampden-Sydney College) Basic CSSLecture 17 Wed, Feb 21, 2018 1 / 22 1 CSS 2 Background Styles 3 Text Styles
More information