Math by Tathagata
The comparison test for series is used to check whether the series is convergent or not. Comparison test is useful when one can compare the given series with another series whose convergence is known. In this article, we learn about comparison test of a series with its limit form and some solved examples. Comparison Test … Read more
For a sequence {an}, if we add all the members of that sequence, then we get an infinite series. Here, a1+a2+a3+… is called infinite series (simply, a series) generated by the sequence {an}. In this article, we will study the convergence of a series along with its definition, formula, examples. The above series is denoted … Read more
The periodic functions are such functions whose values are repeated at regular intervals or periods. The period of a periodic function is its main characteristic. In this article, we study the periodic functions with their examples and properties. Periodic Function Definition A function f(x) is called a periodic function if f(x) is defined for all … Read more
The orthogonal and orthonormal functions on an interval [a, b] are such functions where the tangents to the curves y=Φ1(x) and y=Φ2(x) at their intersecting points are perpendicular to each other. In this article, we study orthogonal and orthonormal functions along with examples. Orthogonal Function Definition A set of functions {Φ1(x), Φ2(x), …, Φn(x), …} … Read more
The even and odd functions are classified by their symmetry properties. A function f is even if f(-x)=f(x) and odd if f(-x)=-f(x). In this article, we study even and odd functions with their properties and solve some problems. Even and odd functions are defined as follows: Even Function: f(-x) = f(x).Odd Function: f(-x) = -f(x). … Read more
The well ordering principle of natural numbers states that every non-empty subset of natural numbers has a least element. Here we state and prove the well-ordering principle with applications. ℕ: = The set of natural numbers. Statement of Well Ordering Principle Every non-empty subset of natural numbers has a least element. That is, if S … Read more
The following problems on Mathematical Analysis can be treated as an assignment for the course MTH275. Please solve the problems (as many as you can) and submit to me. Real Analysis Q1: Prove that √2, √3 are irrational numbers. Q2: State Cauchy’s principle for the convergence of a series. Using this principle show that the … Read more