PPT-Discrete Structures for Computer Science

Presented By Andrew F Conn Lecture 22 Relations and Representations November 28 th 2016 Binary relations establish a relationship between elements of two sets Definition Let and be two sets A . 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic . Surfaces. 2D/3D Shape Manipulation,. 3D Printing. CS 6501. Slides from Olga . Sorkine. , . Eitan. . Grinspun. Surfaces, Parametric Form. Continuous surface. Tangent plane at point . p. (. u,v. ). is spanned by. Dr. Feng Gu. Way to study a system. . Cited from Simulation, Modeling & Analysis (3/e) by Law and . Kelton. , 2000, p. 4, Figure 1.1. Model taxonomy. Modeling formalisms and their simulators . Discrete time model and their simulators . Variational. Time Integrators. Ari Stern. Mathieu . Desbrun. Geometric, . Variational. Integrators for Computer Animation. L. . Kharevych. Weiwei. Y. Tong. E. . Kanso. J. E. Marsden. P. . Schr. ö. 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic . Chapter 1. CISC 2315 Discrete Structures. Professor William G. Tanner, Jr.. Fall 2010. Slides created by James L. Hein. , . author of. Discrete Structures, Logic, and Computability. , 2010, 3rd Edition, Jones & Bartlett Computer Science, . 1. Initially prepared by Dr. . İ. lyas. . Çiç. ekli. ; improved by various Bilkent CS202 instructors.. Graphs. Graphs are one of the unifying themes of computer science.. A graph G = (V. , . E) is defined by a set of . Announcements:. HW . 4. . posted, . due Tues May 8 at 4:30pm. . No late HWs as solutions will be available immediately.. Midterm details on next page. HW . 5 will . be posted . Fri May 11. , . due . Presented by: Andrew F. Conn. Adapted from: Adam Lee. Lecture #6: Proof Methods and Strategies. September 19. th. , 2016. Announcements. HW #1 is due Wednesday. HW #2 will come out today.. It is tentatively due next Wednesday 9/28. Presented . By:Andrew. F. Conn. Lecture #23: N-. ary. relations and Representations. November 30. th. , 2016. Announcements. This is the end of new material!!!. Thank you for sticking it out with me.. Equations. Outline. • Discrete-time state equation from . solution of . continuous-time state equation.. • Expressions in terms of . constituent matrices. .. • Example.. 2. Solution of State Equation. Graph Data Structures " Unless in communicating with it [a computer] one says exactly what one means, trouble is bound to result. " - Alan Turing CLRS, Section 22.1 Early Graph Theory Problem Leonhard Euler (1707 - 1783) Chapter 5. Discrete-Time Process Models. Discrete-Time Transfer Functions. The input to the continuous-time system . G. (. s. ) is the signal:. The system response is given by the convolution integral:. Homologous structures. Human Arm . Bat Wing . Whale Flipper. . Analogous. Structures . Similar functions but NOT structurally related. . Insects are arthropods and birds are vertebrates. . The wing of a bird and the wing of a butterfly are examples of .