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

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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