Applied Mathematics Course and Exercises Second-Year Engineering Students Civil Engineering – Mechanical Engineering – Electrotechnics

Abstract

This course provides a comprehensive introduction to the main concepts of Applied Mathematics for second-year engineering students. It covers simple, double, and triple integrals, together with their fundamental properties, techniques, and engineering applications. Generalized and improper integrals are presented, with emphasis on convergence criteria and important analytical properties. The course develops the theory and methods for solving first- and second-order differential equations and related applications. Numerical, power, and Fourier series are studied, including convergence, uniform convergence, and Parseval-type results. The Fourier transform is introduced through its main properties and applications to signal analysis and differential equations. The Laplace transform is also developed as an effective tool for solving linear differential equations and related problems. Each chapter is supported by solved exercises designed to strengthen students’ understanding and develop their mathematical problem-solving skills.