Math by Tathagata
Tathagata This is the page for Differential Equation practice problems. Here, a list of practice problems will be given for the course on Differential Equation (Exercise). Final Sem Practice Problems The set of practice problems is divided into two parts: Ordinary Differential Equation and Partial Differential Equation. Ordinary Differential Equation Problems Q1: Eliminate A and B … Read more
Here, you can find a list of engineering mathematics questions that can be treated as practice problems in Mid-Sem exam, Sep-Oct 2026. Engineering Mathematics I Mid Term Practice Problems 2026 Q1: Find the following limits: Q2: Find the value of k for which the function f(x) = $\begin{cases} \dfrac{1-\cos 4x}{8x^2} \,\, \text{ if } x … Read more
The particular integral of a differential equation is needed to find to solve the equation. In this article, lets learn how to find particular integral with formula and method. Method of Finding Particular Integral (PI) Let us consider a second order linear differential equation with constant coefficients: $\dfrac{d^2y}{dx^2}+a\dfrac{dy}{dx}+by=Q(x)$ …(1) where a and b constants and … Read more
The general form of linear differential equation of first order is of the form: dy/dx + P(x)y = Q(x) where P(x) and Q(x) are functions of x. Using integrating factor method, we solve this equation. In this article, let us learn how to solve a first order linear differential equation with examples. Integrating Factor of … Read more
A series of the form a0+a1x+a2x2+… = ∑ anxn is called a power series. The radius of convergence of a power series is a very powerful tool in many areas of Mathematics. In this article, we will study the convergence of a power series. Definition of Power Series A series of the form a0+a1(x-a)+a2(x-a)2+… = … Read more
A series ∑an is called absolutely convergent if ∑|an| converges. A series ∑an is called conditionally convergent if it converges but not absolutely. In this article, we study absolute and conditional convergence with their definitions and examples. Absolutely Convergent Series Definition: A series $\displaystyle \sum_{n=1}^\infty a_n$ is called absolutely convergent if the series $\displaystyle \sum_{n=1}^\infty … Read more
An alternating series is a series containing terms alternatively positive and negative. One can check its convergence using Leibnitz’s test. In this article, we will study alternating series, Leibnitz’s test with solved problems. Definition of Alternating Series A series of the form $\displaystyle \sum_{n=1}^\infty$ (-1)n+1an, where an>0 for all n, is called an alternating series. … Read more
Cauchy’s Root test for series is used to test the convergence or divergence of an infinite series. It states that if limn→∞ an1/n is less than 1 then the series ∑an converges and if the limit is greater than 1 then the series diverges. In this article, we will study Cauchy root test of a … Read more
The ratio test for series is useful to check a series is convergent or divergent. Here we consider the limit of the quotient of (n+1)-th and n-th terms of the series, and depending on this limit is greater or less than 1 we decide its convergence. In this article, we study the ratio test of … Read more
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