This book has been written strictly according to the latest syllabus of All Universities of Andhra Pradesh state for B.Sc. Third Year (Vth Semester) students. It covers Beta and Gamma Functions, Chebyshev Polynomials, Power Series Solutions of Ordinary Differential Equations, Hermite Polynomials, Legendre Polynomials, Bessel Functions. The book will guide the students in a proper way and inspire them to sure and brilliant success.