Spring Semester Engineering Mathematics

The document is a comprehensive set of lecture notes for the Spring Semester Engineering Mathematics courses (MAS140, MAS151, MAS152, and MAS156) at the University of Sheffield. It covers key topics in integration, including indefinite integrals, standard integrals, and methods like substitution, integration by parts, and partial fractions. The notes also delve into matrices, linear equations, determinants, eigenvalues, and eigenvectors, as well as ordinary differential equations (ODEs) and Laplace transforms. Detailed examples and exercises are provided to help students practice and understand the material. The document is well-structured, with clear explanations and step-by-step solutions, making it a valuable resource for students studying engineering mathematics.