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Semester 1 Differentiation-Essential Mathematical Skills and Techniques, Lecture notes of Mathematics

The University of SheffieldMathematics

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 examples like the modulus function. A comprehensive list of useful derivatives for various functions, including trigonometric, hyperbolic, and inverse functions, is included. The material is designed to supplement video lectures and is accessible via the course webpage, offering students a solid foundation in differentiation for engineering and mathematical applications.

Typology: Lecture notes

2023/2024

Available from 03/14/2025

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3/14/25, 10:54 PM Semester 1 Differentiation University of Sheffield School of Mathematics and Statistics MAS140: Mathematics (Chemical) MAS152: Civil Engineering Mathematics MAS152: Essential Mathematical Skills & Techniques MAS156: Mathematics (Electrical and Aerospace) MASI61: General Engineering Mathematics Semester 1 2017-18 Outline Syllabus + Functions of a real variable. The concept of a function; odd, even and periodic functions; continuity. Binomial theorem. + Elementary functions. Circular functions and their inverses. Polynomials. Exponential, logarithmic and hyperbolic functions. + Differentiation. Basic rules of differentiation: maxima, minima and curve sketching. + Partial differentiation. First and second derivatives, geometrical interpretation. + Series. Taylor and Maclaurin series, L’Hipital’s rule. + Complex numbers. basic manipulation, Argand diagram, de Moivre’s theorem, Euler’s relation. + Vectors. Vector algebra, dot and cross products, differentiation. Module Materials These notes supplement the video lectures. All course materials, including examples sheets (with worked solutions), are available on the course webpage, http://engmaths.group.shef.ac.uk/mas140/ http://engmaths.group.shef.ac.uk/mas151/ sngmaths.group.shef.ac.uk/mas152/ sngmaths. group shef.ac.uk/mas156/ /engmaths. group shef.ac.uk/mas161/ which can also be accessed through MOLE. about:blank