Math by Tathagata
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 study material of Special Functions are given on this page. Special Functions Practice Problems. Some practice problems of Special Functions are given here. Mid Term Practice Problems 2026 Q1: Define beta and gamma functions. Q2: What are the value of $\Gamma(6)$ and $B(4, 5)$? Q3: Prove that $\Gamma(n+1)=n \Gamma(n)$, and hence prove $\Gamma(n+1)=n!$ Q4: … Read more
The Cayley-Hamilton theorem is about the characteristic equation of a square matrix. Using this theorem one can find the inverse of a matrix, the integral power of a matrix, and many more. In this post, we will study this theorem along with some applications. Cayley-Hamilton Theorem Statement Statement: Every square matrix satisfies its own characteristic … Read more
The characteristic equation of a matrix is an important tool to study a matrix. Using this equation, we can find the eigenvalue with its corresponding eigenvectors to analyse a matrix. In this post, we will learn about the characteristic equation of a matrix. Definition Let A be an n×n matrix over a field F. The … Read more
Rolle’s theorem is very useful in Calculus for continuous functions. In this post, we will learn Rolle’s theorem with its geometrical interpretation along with some solved examples. Statement of Rolle’s Theorem Let f(x) be a real-valued function defined on the closed interval [a, b] satisfying the following: Then there is a point c ∈ (a, … Read more
The nth derivative of a function f(x) is obtained by by successively differentiating f(x) n times with respect to x. The Leibnitz theorem is a powerful tool to find it for a product function. In this post, we will learn how to find n-th derivative of a function with examples. Definition of nth Derivative The … Read more
On this page, you can find syllabus, best books on Engineering Mathematics I, and practice problems. Study material on Engineering Mathematics 1 is also given here. My Amazon StoreFront Differential Calculus Integral Calculus Linear Algebra Vector Algebra My Amazon StoreFront Books You can follow Higher Engineering Mathematics Book by B S Grewal that help you … Read more