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Below are few calculus  Questions which  I solved..  (1)Find the derivative of the following if: (i) 2y²=x²siny+xy³ (ii)x²y²+4xy+x-6y=2 (2)differentiate y=cos-¹(4x³-1) (…

The  Ga ussian integral or otherwise known as the Euler-poisson integral of the Gaussian function e^(-x^2) over  the entire real line. The integral is: The …

Special functions like the exponential functions are integreable, the formula for integrating exponential functions is: Integrating exponential functions using a s…

Integrating Trigonometric Functions is one of the major aspects of Integral Calculus, trigonometric functions have standard integral values on the table of integrals. B…

I Come to think of it.. What do we understand by rational functions . A Rational Function is a function expressed as a fraction with  polynomials as its numerator an…

integration is another beautiful aspect of calculus.. Integration is defined to be the reverse of differentiation .. Integration can be solved by different methods d…

A qoutient function is a function expressed in terms of division for exam a/b. Hence in differentiation any function expressed in terms of qoutient are usually evaluat…

Here we give a little bit more difficult example of the product formula of differentiation.. We can see clearly that the first function here (x³+2)² is not a function we…

The product rule is simple and very interesting to use.. All you need to do is to define your given functions in terms of the variables of the product formula. You fir…

Example 2: find the derivative of (3χ²+4x)⁴ Solution : we simply use chain Rule because the function is defined in terms of powers. Chain Rule formula : dy/dx= dy/…

Rule 2: the chain Rule This rule is quite simple and easy it defined by: dy/dx= dy/du × du/dx To carry out chain Rule in any given function then that function must b…

differentiation is simple  in fact we can say  it's the simplest aspect or topic of mathematics.. But to carry out differentiation we need to know the rules. Rule1:…

Mathematics is a branch of science that deals with the study of topics such as quantity (numbers ),  structure,  space , and change . Mathematicians seek out patterns …

Mapping and Function Assignment Mapping: suppose we can assign each element x of a set X in a way, a unique element y of a set Y written as y = f(x) then this is called…

The overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems, the variety …

Basic math SEQUENCES AND SERIES Sequences: the topic of sequences is an aspect of mathematics that is widely treated in the field of real analysis, generally s…

ALGEBRA OF GROUPS                                 GROUPS THEORY         Excerpted from Beachy/Blair, Abstract Algebra , 2nd Ed. , © 1996 …

Discrete Mathematics.pdf

Graph Theory: Definition and Properties Authors: Dr. Jean-Paul Rodrigue and Dr. Cesar Ducruet 1. Basic Graph Definition A graph is a symbolic representation of a netw…

Real analysis  (traditionally, the  theory of functions of a real variable ) is a branch of  mathematical analysis  dealing with the  real numbers  and real-valued funct…