Book excerpt: Mathematics - I has been written specifically for the first year Gujarat Technological University (GTU) syllabus and students of all programs of engineering since first semester mathematics is common to all branches. It covers Indeterminate Forms, Gamma and Beta Functions, Applications of Definite Integrals, Sequences and Series, Taylor's and Maclaurin's Series, Fourier Series, Partial Derivatives, Multiple Integrals, and Matrices for the benefit of the students.