Spring Semester Engineering Mathematics

The document is a detailed set of lecture notes for the Spring Semester Engineering Mathematics courses (MAS140, MAS151, MAS152, and MAS156) at the University of Sheffield. It covers essential topics in integration, including indefinite integrals, standard integrals, and techniques like substitution, integration by parts, and partial fractions. The notes also explore matrices, linear equations, determinants, eigenvalues, and eigenvectors, as well as ordinary differential equations (ODEs) and Laplace transforms. Each section is supported by clear examples, exercises, and step-by-step solutions, making it a practical resource for students. The material is well-organized, with a focus on both theoretical understanding and practical application, helping students build a strong foundation in engineering mathematics.