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

The document is a study guide on partial differentiation, likely part of a first-semester mathematics course such as MAS152: Essential Mathematical Skills and Techniques. It introduces the concept of functions of multiple variables, focusing on two-variable functions like \( z = f(x, y) \), and explains how to compute partial derivatives with respect to each variable while holding the others constant. The guide includes examples of finding first and second-order partial derivatives, using rules like the **product rule** and chain rule. It also covers higher-order derivatives and their notations, such as \( \frac{\partial^2 f}{\partial x^2} \) and \( \frac{\partial^2 f}{\partial x \partial y} \). The document is practical, with step-by-step solutions and graphical interpretations, making it a valuable resource for understanding multivariable calculus.

Typology: Study notes

2024/2025

Available from 03/14/2025

charles-khama
charles-khama 🇮🇹

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Download Semester 1 Partial Differentiation-Essential Mathematical Skills and Techniques and more Study notes Mathematics in PDF only on Docsity!

3/14/25, 10:53 PM Semester 1 Partial 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’Hépital’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