Math by Tathagata
Tathagata 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 following questions on Complex Analysis can be treated as an assignment as well as the suggestions on the upcoming exam. Q1: Find the real and the imaginary part of $f(z)=\dfrac{\overline{z}}{z}, z \neq 0$. Q2: Define the differentiability of a function f(z) at z=z0. Prove that f(z) = |z| is not differentiable at z=0. Q3: … 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
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
The following are the assignments for the upcoming exam on Engineering Mathematics I. Please solve the questions and submit. Some Study Material: ** End Sem Syllabus: Unit I , II, III, and IV. Unit I and IV: Differential Calculus & Vector Algebra Note: This section is for Sec G and Sec L. Q1: Show that … Read more