Advanced Mathematics for Science and Technology

This book presents the fundamental concepts essential to the second-year mathematics program in science and technology. The first chapter thoroughly explores integral calculus, including the Riemann integral, double and triple integrals, and their applications in calculating areas and volumes. The second chapter addresses improper integrals and their properties. The third chapter is dedicated to ordinary differential equations, focusing on linear differential equations of the first and second order, as well as partial differential equations. The fourth chapter delves into numerical series, sequences and series of functions, power series, and Fourier series. In the fifth chapter, we introduce the Fourier transform and its properties. The sixth chapter covers the Laplace transform, its properties, and its application in solving differential equations. Each chapter is accompanied by a series of exercises designed to reinforce the understanding of the presented concepts.