Book excerpt: Mathematics - II has been written specifically as per the Gujarat Technological University (GTU) syllabus and for First Year (Second Semester) students of all programmes of engineering. It covers important topics such as Vector Calculus, Laplace Transform and Inverse Laplace Transform, Fourier Integral, First Order Ordinary Differential Equations, Ordinary Differential Equations of Higher Orders, and Series Solutions of Ordinary Differential Equations and Special Functions to help students gain a deep-rooted understanding of the key elements of the subject which would help students to build their self-confidence which is the key aspect in learning.