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

The document is a set of lecture notes for MAS152: Essential Mathematical Skills and Techniques, focusing on vectors during Semester 1 at the University of Sheffield. It covers the basics of vector algebra, including addition, subtraction, scalar and vector products, and rectangular resolution. The notes also explore unit vectors, determinants, and differentiation of vectors, with applications in dynamics such as velocity and acceleration. The material is supplemented with examples and step-by-step solutions, making it a comprehensive resource for understanding vector operations and their applications in mathematics and engineering.

Typology: Lecture notes

2024/2025

Available from 03/14/2025

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Download Semester 1 Vectors-Essential Mathematical Skills and Techniques and more Lecture notes Mathematics in PDF only on Docsity!

3/14/25, 10:57 PM about:blank MASI40: MASI52: MASIS2: MASIS56: MASIO61: Semester 1 Vectors University of Sheffield School of Mathematics and Statistics Mathematics (Chemical) Civil Engineering Mathematics Essential Mathematical Skills & Techniques Mathematics (Electrical and Aerospace) 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 Mat These notes supplement the video lectures. All course materials, including examples sheets s (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. 14