Mathematics

Wednesday, January 13, 2016

Mid-Term Suggestion for 15th Batch

Suggestion of Mid-Term Examination for 15^th Batch

Chapter	example	Exercise
3	8,7,10	3(1)(2), 5(i)(iv), 7(i)(ii), 11(v), 16(i)(ii)
4	6,10,11,15	1(iv)(vii), 4(i)(iii), 7(i)(iii), 10(i)(ii), 12(i)(ii)
5	4,5,7,13	2(i), 3(i), 4(i)(iv), 5(i)(iii), 7(i), 8(i), 9(iii), 15
8	1,5,11	10,11,13,24,25
9	6,10,11	9(viii)(xiii), 2(i), 3(i)(iii), 6(i)(vii), 9(i)(ix)(xii)
11	7(ii)(v), 8(ii)(iii)	2(i)(iv), 4(i)(iv), 7(i), 9(i), 12(i), 14(i)
12	3,5,6,8 12,17,18,20	13,15,20,21,26-30

Monday, January 11, 2016

Math Syllabus for CSE 16th Batch

You can easily calculate your in-course mark

Quiz-1

(15)

Quiz-2

(15)

Quiz-3

(10)

(30)

Mid (40)

Final

(80)

Total

(200)

Gain(20)

(200/10 = ?)

CSE-115 Differential Calculus and Co-Ordinate Geometry
3 hours in a week, 3.00 Cr.

Differential calculus: Limits, continuity and differentiability; successive differentiation of various types of functions; Leibniz’s theorem; Role’s Theorem; Mean value Theorem in finite and infinite forms; Lagrange’s form of remainders; Cauchy’s form of remainders; Expansion offunctions; Evaluation indeterminate forms by L Hospitals rule; Partial differentiation;

Euler's Theorem; Tangent and Normal, Subtangent and; subnormal in Cartesian and polar co-ordinates; Maximum and minimum values of functions of single variable; Points of inflexion; curvature, radios of curvature, center of curvature Asymptotes, curve tracing.

Co-ordinate Geometry: Transformation of co-ordinates and it uses; Equation of conies and its reduction to standard forms; Pair of straight line & Homogeneous equations of second degree; Angle between a pair of straight lines; Pair of joining the origin to the point of, intersection of two given curves, circles; system of circle, orthogonal circles; radical axis, radical center, properties of radical axes; Coaxial circle and limiting points; Equations of parabola, ellipse and hyperbola in Cartesian and polar coordinates; Tangents and normals, pair of tangents; Chord of contact; Chord in terms of middle points; Pole and polar parametric co-ordinates; diameters; Conjugate diameter and their properties; Director circles and asymptotes.

Reference books:
1. Dr. Abdul Matin, Differential Calculus.
2. Abu Yusuf, Differential Calculus Integral Calculus.
3. B.C Das & B.N. Mukherjee, Differential calculus.
4. A textbook of Co-ordinate Geometry (two and three dimensions).
5. Rahman and Bhattacharja, Co-ordinate Geometry and Vector analysis.

Defination(Number) for BBA 16th Batch

Digit

Decimal Number System : 0,1,2,3,4,5,6,,7,8,9

Binary Number System : 0, 1

Octal Number System : 0, 1,2,3,4,5,6,7

Hexadecimal Number System : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E

Integer

An integer is a number that can be written without a fractional component.

Positive Integer : 1, 2, 3,…………,300,…4000,

Zero : 0 (non positive, non negative integer)

Negative Integer : -400, …., -100,…,…. -4, -3, -2,

Natural Number

The natural numbers are those which are used for counting and ordering.

For example: 0,1,2,3,4,5,6…….

Irrational Number

An irrational number is any real number that cannot be expressed as a ratio of integer.

For example: √2, √3, √7 I √prime number

Rational Number

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers , p and q, with the denominator q not equal to zero.

For example: 4, 200, -21, 9.75, 1.33,

Real number

A real number is a value that represents a quantity along a continuous line.

Complex Number

A complex number is a number that can be expressed in the form a + bi, where a and b are real number and i is the imaginary unit.

Imaginary unit

The imaginary unit denoted as i, is a mathematical concept which extends the real number system ℝ to the complex number system ℂ . The imaginary unit's (that satisfies the equation x² = −1) core property is that i² = −1, i,e i= √-1

For example: √-2, √-4, 0+√-4, 3-√-8, I √negative value

All Definition for CSE 16th Batch

Function

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Example:

Let f(x)=x²be a function, if the input is −3, then the output is 9, and we may write f(−3) = 9. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9.

Undefined
A function is said to be "undefined" at points not in its domain. For example, in the real number system,

f(x)={\sqrt {x}}

is undefined for negative

x

, i.e., no such values exist for function

f

.
The set of numbers for which a function is defined is called the domain of the function. If a number is not in the domain of a function, the function is said to be "undefined" for that number. Two common examples are

f(x)={\frac {1}{x}}

, which is undefined for

x=0

, and

f(x)={\sqrt {x}}

, which is undefined (in the real number system) for negative

x

.

Limit
limit is the value that a function or sequence "approaches" as the input or index approaches some value.Limits are used to define continuity, derivatives and integrals.

Indeterminate form
If the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form.
The indeterminate forms typically considered in the literature are denoted 0/0, ∞/∞, 0 × ∞, ∞ − ∞, 0⁰, 1^∞ and ∞⁰.

Wednesday, October 21, 2015

Link for inserting mathematical Equation in Blog

Inserting Mathematical Equation is little difficult, But not impossible. If we follow the following instruction, we can easily insert the Mathematical Equation on Blog.

Fist type $

Insert mathematical code from the given link

Finally again type $

Remember, Don't give any Space after/before typing $

Link-https://www.codecogs.com/latex/eqneditor.php

Example:
$\sqrt[4]{5}$
$a^{5}$
$ax^{2} + b^{2}$

Tuesday, October 20, 2015

Mathematical Symbol

$+ \!\,$	Addition	$- \!\,$	Subtraction
$\times \!\,$ or $\cdot \!\,$	Multiplication	$\div \!\,$ or $/ \!\,$	Division
$\int \!\,$	Integration	$\oint \!\,$	integration is over a closed surface
$\therefore \!\,$	Therefore, so. hence	$\because \!\,$	Because, Since
$\sqrt{\ } \!\,$	Square root	$\sqrt[4]{5}$
$\infty \!\,$	Infinity	$\propto \!\,$	Proportion
$=$	is equal to	$\ne$	is not equal to
$\approx$	approximately equal	$\sim$	is similar to
$\Leftrightarrow$	if and only if	$\Rightarrow \!\,$	implies; if ... then
$<$	is less than	$\ll \!\,$	is much less than
$>$	is greater than	$\gg \!\,$	is much greater then
$\le \!\,$	is less than or equal to	$\ge$	is greater than or equal to
$\subseteq \!\,$	sub set	$\supseteq \!\,$	super set
$\| \ldots \| \!\,$	absolute value of; modulus of	${\{\ ,\!\ \}} \!\,$	the set of ...
$\forall \!\,$	for all	$\exists \!\,$	there exist
$\in \!\,$	is an element of;	$\notin \!\,$	is not an element of



$\mathbb{C} \!\,$	Complex number	$\mathbb{N} \!\,$	Natural number
$\mathbb{R} \!\,$	Real number	$\mathbb{Z} \!\,$	Integer
$\mathbb{Q} \!\,$	Rational number	$\mathbb{Q} \!\,$	Irrational number