Indian Institute of Technology Guwahati
Solution to Tutorial Sheet 2
Jan-April 2017 semester
MA 102, Mathematics II
Ans 1: (a) Dividing by (1 + x)y we can write dy
y =
that
Z
Z
dx
dy
=
y
1+x
dx
(1+x) .
Therefore, it follows
ln|y| = ln|1 + x| + c1
|y| = ex
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
CSN-523: Computational Geometry
Lecture 1: Introduction
Dr. Sudip Roy
Assistant Professor
Department of Computer Science & Engineering
Piazza Class Room: https:/piazza.com/iitr.ac.in/spring2017/csn523/home
Moodle Sit
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 39
Last Lecture
Instructor : Surender Baswana
1
Which of the two algorithms would you call faster than the other?
Algorithm A worst case number of instructions : 10n + 200
Algorithm B worst ca
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 37
Analyzing the efciency of algorithms.
Algorithms compared
Sequential Search and Binary search
GCD fast and GCD slow
Merge Sort and Selection Sort
1
Problem 1 : Searching
2
Comparing Sear
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 38
Analyzing the number of steps in Quick Sort.
Why the exact values of constants in an + c are ignored
Time Complexity of algorithms.
Examples .
1
Number of instructions taken in Quick Sort
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 36
Announcement : Extra sessions for lab test
Sorting algorithms based on recursion
Quick Sort (did in lst class)
Merge Sort
Introduction to Time Complexity
1
Extra session for lab
On Sunda
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 35
Input from keyboard and output to Console : (Lecture 34)
Input and Output from/to le
(using the existing classes and method of package java.io.*)
Sorting algorithms based on recursion
Qui
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 34
Fun : Tower of Hanoi - a classical recursive problem
Binary Search
Input/Output - Part 1
(using the existing classes and method of package java.io.*)
1
Tower of Hanoi
There are three Towe
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 33
Clarifying doubts from previous lecture
Proving correctness of a recursive method
More examples of recursion
Input/Output (if time permits)
Note I have tried to simplify these slides afte
Proving correctness of Recursive methods
as part of Lecture 33
As an example, we consider the method PatternS(int n, int m, String S). We shall prove that this recursive
method is indeed correct, that is, it prints all strings of the form S+P with n |s an
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 31+32
Solving problems recursively
Examples
Implementation of Recursion involves method calling itself. So it is
essential that you FULLY understand the invocation of methods from
Lecture 30 t
ESC101 : fundamental of computing
Lecture 28
17 October, 208
In this lecture we continued discussion on Arrays. We gave description of
the following programs.
1. Generating random number
(see the le random example.java)
Those who are interested in the mat
Arrays of Objects
Parallel array solution:
rollNum=
cfw_6016, 6024, 6078;
midsemMarks = cfw_61.7, 54 , 74.2 ;
name =
cfw_"Abhishek Murthy", "Abhishek Singh",
"Ankit";
In practice, parallel arrays are hard to maintain.
Better: define class STUDENT with att
Types in Java
8 Primitive Types
byte, short, int, long
float, double
boolean
Char
Object types:
predefined e.g. String ;
User-defined via class and constructors
What if we want to store lots of items e.g.
midsem marks?
Primitive Type Syntax
double numb
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 24
Object Oriented programming
Quiz (access control for a member of class)
Static attribute/eld of a class
Static method of a class
1
Access control
access control is performed on a per clas
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 22
Object Oriented programming
Building complex classes using simple classes
Packages (library of related classes)
Example with Object reference as parameters in Methods
Access controls (pub
ESc101 : Fundamental of Computing
I Semester 2008-09
Lecture 22
Object Oriented programming
Method Overloading in Java.
Constructor
Building complex classes using Point class
Circle, Triangle,.
1
Method overloading in JAVA
Question : In a class, can th
CMPS 6640/4040 Computational Geometry
Spring 2016
Plane Sweep Algorithms
Carola Wenk
3/3/16
CMPS 6640/4040 Computational Geometry
1
Line Segment Intersection
Input: A set S=cfw_s1, , sn of (closed) line
segments in R2
Output: All intersection points bet
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
CSN-523: Computational Geometry
Lecture 8: Art Gallery Problem and Related Discussions
Dr. Sudip Roy
Assistant Professor
Department of Computer Science & Engineering
Piazza Class Room: https:/piazza.com/iitr.ac.in/sp
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
CSN-523: Computational Geometry
Lecture 9: Data Representation for Geometric Problems
Dr. Sudip Roy
Assistant Professor
Department of Computer Science & Engineering
Piazza Class Room: https:/piazza.com/iitr.ac.in/spr
DEPARTMENT OF MATHEMATICS, IIT - GUWAHATI
Even Semester of the Academic year 2016 - 2017
MA 102 Mathematics II
Problem Sheet 3: Higher order ODEs, initial and boundary value problems,
homogeneous and nonhomogeneous equations, higher order equations with
c
Indian Institute of Technology Guwahati
Solution to Tutorial Sheet 3
Jan-April 2017 semester
MA 102, Mathematics II
Ans 1: If y(x) = c1 + c2 x2 should satisfy the conditions y(0) = 0 and y (0) = 1,
then we must have c1 + c2 .0 = 0 and 2c2 .0 = 1. This imp
Indian Institute of Technology Guwahati
Solution to Tutorial Sheet 1
Jan-April 2015 semester
MA 102, Mathematics II
Ans 1: (a) Order:4, Degree:1, nonlinear. (b) Order:2, Degree:1, nonlinear.
(c) Order:2, Degree:1, linear. (d) Order:2, Degree:2, nonlinear.
DEPARTMENT OF MATHEMATICS, IIT - GUWAHATI
Even Semester of the Academic year 2016 - 2017
MA 102 Mathematics II
Problem Sheet 4: Method of undetermined coefficients, annihilator approach
(operator method), variation of parameters.
Instructor: Dr. J. C. Kal
DEPARTMENT OF MATHEMATICS, IIT - GUWAHATI
Even Semester of the Academic year 2016 - 2017
MA 102 Mathematics II
Problem Sheet 2: First order ODEs, Exactness, Variable separable,
Integrating factor, Bernoullis equation.
Instructor: Dr. J. C. Kalita and Dr.
Sensory systems
sensory systems - hearing, taste, smell and
visual receptors
i) Mechanism of hearing, sound pressure,
mechanism of hair cell activation, cochelea
ii) Sense of Taste, Sensory neurons, Capsaicin
iii) Sense of smell: Characteristic properties
Diversity in biological systems
The variety of life on Earth and the essential
interdependence of all living things
What is living?
[Selflf replicating,
[S
li ti
evolving
l i and
d self-regulating
lf
l ti iinteracting
t
ti systems
t
capable of responding
Physics II: Electromagnetism
PH 102
Lecture 2
Sayan Chakrabarti
Indian Institute of Technology Guwahati
[email protected]
January-May 2017
Some identities involving Gradient ,
Divergence and Curl
~ A
~ + B)
~ = r.
~ A
~ + r.
~ B
~
r.(
~ (A
~
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
CSN-523: Computational Geometry
Lecture 6: Art Gallery Problem
Dr. Sudip Roy
Assistant Professor
Department of Computer Science & Engineering
Piazza Class Room: https:/piazza.com/iitr.ac.in/spring2017/csn523/home
Moo