MAS152

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 Lapl...

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 Lap...

The document is a set of lecture notes on differentiation for Semester 1, covering multiple courses (MAS140, MAS151, MAS152, MAS156, and MAS161) at the University of Sheffield. It provides a detailed introduction to differentiation, including definitions, rules (product, quotient, chain, and inverse function rules), and applications, such as finding maxima, minima, and points of inflection. The notes also discuss the relationship between continuity and differentiability, illustrated with example...

The document is a set of lecture notes on differentiation for Semester 1 , covering multiple courses (MAS140, MAS151, MAS152, MAS156, and MAS161) at the University of Sheffield. It provides a detailed introduction to differentiation, including definitions, rules (product, quotient, chain, and inverse function rules), and applications such as finding maxima, minima, and points of inflection. The notes also discuss the relationship between continuity and differentiability, illustrated with example...

The document is a formula sheet for the courses MAS140, MAS151, MAS152, MAS156, and MAS161, at the University of Sheffield. It serves as a comprehensive reference for students, covering essential mathematical formulas and results that can be quoted without proof in exams. The sheet includes key topics such as trigonometry, hyperbolic functions, series expansions (arithmetic, geometric, and binomial), differentiation rules, and integration techniques. Additionally, it provides Laplace transforms...