Mathematical Methods for Chemical and Environmental Engineering

Code

MATH1047

School

School of Mathematical Sciences

Level

1

Credits

20

Semesters

Full year China

Summary

This module covers: 

• use and manipulate matrices; 
• provide graphical representation and characterisation of curves and functions;
• demonstrate knowledge and application of differential and integral calculus; 
• apply a range of integration techniques to functions of a single variable; 
• apply differential and integral calculus to simple engineering problems;
• write code in Python to solve simple numerical problems including, but not restricted to, solving quadratic equations, solving equations of the form f (x) = 0, solving linear systems using row operations, approximating derivatives numerically, approximating integrals numerically
• manipulate vectors to solve geometric problems in engineering;
• classify and solve a range of standard-type first-order ordinary differential equations 
• understand and apply basic differential calculus associated with functions of several variables; 
• apply differential operators to scalar and vector fields relevant to engineering problems; 
• apply suitable numerical methods to finding zeros of functions and to solving first order differential equations.

Target Students

BEng Hons Chemical Engineering and BEng Hons Environmental Engineering and BSc Hons Chemistry students

Classes

• One 1-hour workshop each week for 24 weeks
• One 1-hour lecture each week for 24 weeks
• One 1-hour computing each week for 24 weeks

Assessment

• 5% Coursework 1: Python
• 5% Coursework 2: Linear Systems / Calculus of one variable
• 5% Coursework 3
• 5% Coursework 4
• 80% Exam 1 (3-hour): Written examination

Assessed by end of spring semester

Educational Aims

Learning Outcomes

A2.3.2    Be competent in the use of numerical and computer methods, including commercial software for solving chemical engineering problems (detailed knowledge of computer coding is not required). 

A1.2.1    Have a knowledge and understanding of mathematics necessary for the analysis of and to support applications of key chemical engineering principles and processes. 

A5.2.1    Have developed a wide range of problem-solving skills. 

A5.2.2    Have developed a range of effective communication skills including written reports and presentations. 

A5.2.3    Recognise the importance of working inclusively and effectively with others from a diverse range of backgrounds and have acquired a range of experience in achieving this. 

A5.2.4    Recognise the importance of leadership skills and have had some opportunity to acquire these. 

A5.2.5    Be effective users of IT.

These learning outcomes will be achieved as evidenced by the module content and assessment: 

Matrices and systems of equations
Systems of linear equations
Gaussian elimination
Matrices
Matrix algebra
Zero and identity matrices
Inverse matrix
Determinants of2×2and3×3matrices
Properties of determinants
Row reduction methods
Inversion by Gauss–Jordan method
Eigenvalues and eigenvectors

Calculus of functions of one variable
Functions – domain and range
Limits
Curve sketching
Exponential and logarithm
Hyperbolic functions
Rules for differentiation
Taylor’s theorem    
Maclaurin and Taylor series
Classification of stationary points
Definition of an integral
Integration as anti-differentiation
Integration by parts
Integration by substitution
Applications of integration

Computer Programming (Python)
Variables and variable types
If/While Loops
Range
Plotting and Graphing
Conditional Statements
Root finding using the Method of Bisection
Matrix Inversion and Solving Linear Systems using Row Operations
Numerical Differentiation
Numerical Integration

Conveners