## Engineering Mathematics 1

 Unit code: CHEN10011 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

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#### Aims

Develop the ability to apply the basic principles and methods of calculus and statistics to the types of problems encountered in their study of Chemical Engineering. Learn how to scrutinise a problem to identify the key variables and the most suitable mathematical technique to apply.

#### Overview

¿   Differentiation - Rule of differentiation including product, quotient and chain rules. and . Differentiating key functions including polynomials, trigonometric, exponential and logarithmic functions. Finite difference approximation to derivatives. Applying differentiation with l’Hopital’s Rule, Taylor and McLaurin series, and for numerically finding roots of nonlinear equations with the bisection method and Newton Raphson method. Extension to function of two or more variables including first and higher partial derivatives.

¿   Integration - Rules of integration for functions including polynomials, trigonometric, exponential and logarithmic, Finding the constant of integration. Integrals with limits, integration by substitution and by parts.

¿   Probability - Concept of probability, axioms of probability and probability density functions.

¿   Statistics - Analysis of data and plotting graphs. Mean, standard deviation and coefficient of variation. Histograms and frequency distributions. Errors and error propagation, Regression and correlation. Least-squares fitting.

#### Teaching and learning methods

Teaching is through traditional lectures and problem solving tutorials. Students are given a handout at the beginning of the module. All notes (including slides) are available on blackboard and completed sections of lecture notes are provided periodically throughout the module.  Learning is assisted through supporting information during lectures, blackboard based discussion forum and podcasts.

#### Learning outcomes

 ·         Recognise, interpret and manipulate different types symbols and expressions in calculus equations.·         Apply the rules of calculus to equations in order to find solutions to problems.·         Interchange symbols used in equations with alternative symbols.·         Interpret real engineering problems and identify key variables and processes and represent these as calculus equations which can then be solved.·         Be able to identify the different types of variable and errors in an engineering situation and use them to quantify uncertainty or justify making informed decisions.·         Take experimental or process data and analyse this in a variety of ways visually and statistically, both from first principles and using software such as MS Excel, in order to find meaning within it.

#### Assessment Further Information

 Assessment task Length Weighting within unit (if relevant) Coursework (Diagnostic follow-up and online assessment) Examination ---------------  1.5 hours 20%  80%

·         Stroud, K. and Booth, D. (2003). Engineering mathematics. Basingstoke [u.a.]: Palgrave.

·         Finlayson, B., Biegler, L. and Grossmann, I. (2006). Mathematics in Chemical Engineering. Ullmann's Encyclopedia of Industrial Chemistry.  Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/14356007.b01_01.pub2/pdf

·         Denn, M. (2012). Chemical engineering. Cambridge: Cambridge University Press.

Albright, L. (2009). Albright's chemical engineering handbook. Estados Unidos: Taylor & Francis Group, LLC.

#### Study hours

• Lectures - 16 hours
• Tutorials - 8 hours
• Independent study hours - 76 hours

#### Teaching staff

Peter Martin - Unit coordinator

Abdullatif Alfutimie - Unit coordinator