## 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

None

#### Aims

To explain the basic principles and methods of mathematics (Statistics and Calculus) necessary for first year students in their study of Chemical Engineering.

To help students acquire practical applicable as well as transferrable knowledge on solving concrete problems including the application of mathematical methods in the laboratories.

Specifically, to gain competency in the variety of skills required for subsequent chemical engineering courses in mathematically oriented topics.

#### Overview

Statistics  (This part is taught by Dr Patricia Scully [PS])

Lecture 1: Analysis of data and plotting graphs.

Lecture 2: Mean, standard deviation and coefficient of variation.

Lecture 3: Histograms and Frequency Distributions.

Lecture 4: Concept of probability, Axioms of probability, Probability density functions.

Lecture 5: Errors and error propagation,

Lecture 6: Regression and correlation, Least-squares fitting.

Calculus

Differentiation   (This part is taught by Dr Patricia Scully [PS])

Lecture 7-Basics of Differentiation Rules (Differentiating polynomials, Differentiating trigonometric functions, Differentiating  exponential and logarithmic functions, Differentiating a sum).

Lecture 8-Derivative Rules (The product and quotient rules, the chain rule, the first derivative, the second derivative, Higher-order derivatives, Finite difference approximation to derivatives)

Lecture 9 Revision

#### Teaching and learning methods

To integrating a variety of methods including e-Learning and assessment (Nearpod), raffle quiz, brainstorming and use of multimedia in teaching the module.

To demonstrate for the students how the chemical engineer can bring together the fundamentals to build and refine a mathematical model of a process that will help them understand and optimise its performance. This can be done through the building up of the practical examples (see the syllabus) through the lectures and the applications of which through tutorials. (Experiential learning).

To link the process of teaching and learning to the school recommendations of integrating into the module teaching the following enrichment means: Enquiry-Based-Learning, problem-solving, post lectures notes via Blackboard, access to podcasts and model answers to pervious year exams.

#### Learning outcomes

 Category of outcome Students should/will (please delete as appropriate) be able to: Knowledge and understanding Understand the basics of statistics and calculus. Understand the different types of variable and the different types of error. Develop the ability to inquire information in order to solve mathematical and engineering problems by using basic rules. Intellectual skills Understand and apply statistics and calculus to solve applied chemical engineering and real-world problems. Practical skills Use L'Hospital's rule to evaluate certain indefinite forms.Differentiate functions of one or more variablesExpand functions in series formManipulate partial derivativesObtain numerical solutions to problems in some important engineering subject areas Transferable skills and personal qualities Apply mathematical skills to solve relevant engineering problems. Develop the ability to apply and transfer the basic methods and the acquired skills and knowledge in present and future contexts.

#### Knowledge and understanding

Understand the basics of statistics and calculus.

Understand the different types of variable and the different types of error.

Develop the ability to inquire information in order to solve mathematical and engineering problems by using basic rules

#### Intellectual skills

Understand and apply statistics and calculus to solve applied chemical engineering and real-world problems.

#### Practical skills

Use L'Hospital's rule to evaluate certain indefinite forms.

Differentiate functions of one or more variables

Expand functions in series form

Manipulate partial derivatives

Obtain numerical solutions to problems in some important engineering subject areas

#### Transferable skills and personal qualities

Apply mathematical skills to solve relevant engineering problems.

Develop the ability to apply and transfer the basic methods and the acquired skills and knowledge in present and future contexts.

#### 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

Patricia Scully - Unit coordinator

Abdullatif Alfutimie - Unit coordinator