This is a preview. Log in through your library . Abstract The inverse-function theorem is generalized to multivalued functions of the form f(x) + K, where f is a differentiable single-valued function ...

Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...

In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

Hypergeometric functions are at the heart of many analytical and applied mathematical investigations. These functions, generally defined via power series that extend the geometric series, have been ...

The GATE syllabus for Mathematics (MA) 2025 consists of questions from topics such as Calculus, Linear Algebra, Real Analysis, Complex Analysis, Differential Equations, Algebra, Functional Analysis, ...