Applied Mathematics 1

This document contains comprehensive, chapter-wise detailed notes for Applied Mathematics–I, designed specifically for First Year B.Sc. Information Technology (Semester 1) students under the CBCS (Choice Based Credit System) pattern of the University of Mumbai. It covers all major concepts, definitions, theorems, formulas, and problem-solving techniques required for university examinations. The notes begin with a complete explanation of Functions, including domain, range, types, composite and inverse functions. They then progress into Limits and Continuity, with standard limits, evaluation techniques, and different forms of discontinuity. A thorough section on Differentiation follows, containing standard derivatives, rules such as product, quotient, and chain rule, and real-life applications like maxima, minima, and rate of change. The document also includes a dedicated chapter on Matrices, covering types of matrices, operations, determinants, properties, cofactor, adjoint, and the process of finding matrix inverses. The Linear Algebra section introduces vector spaces, linear independence, basis, dimension, and related vector concepts essential for higher mathematics. The final chapter deals with Differential Equations, explaining order and degree, variable separable method, linear differential equations, integrating factor, and solution techniques. Designed in a clear, simplified, and student-friendly manner, this document serves as a complete study guide for mastering the subject and scoring well in examinations. It is suitable for revisions, self-study, and conceptual learning, making it an essential resource for all B.Sc IT students.