Mathematics for Chemical Engineers 1

Overview

Detailed Syllabus –– Lectures (24 Hours):

Note: The following topics may be slightly rescheduled to meet the class requirements or due to unforeseen contingencies.



Differentiation 1 (2 hrs):

Differentiation rules; Local behaviour of functions; finding the tangent line; definition of the derivative;

Differentiation 2 (2 hrs):

Derivatives polynomials and simple functions; Newton's method to find the roots of an equation; higher derivatives.

Differentiation 3 (2 hrs):

Newton's method to find the roots of an equation; higher derivatives.

Differentiation 4 (2 hrs):

Derivatives of rational function; differentiation of complicated expressions (tricks); partial differentiation; differentiation of implicit functions (thermodynamic applications).

Differentiation 5 (2 hrs):

Geometric application of the derivatives; minima and maxima; inflection points; Taylor series (local approximation and extrapolation); Taylor series of complicated expressions (tricks).

Integration 1 (2 hrs):

The problem of measuring area; thermodynamic examples; the construction of the integral (Riemann); integration as the inverse of differentiation; simple integrals; indefinite and definite integrals.

Integration 2 (2 hrs):

Basic Integration rules; integration by substitution;

Integration 3 (2 hrs):

Integration by parts; integration by partial fraction; Integrations of common functions (tricks); improper integrals.

Integration 4 (2 hrs)

Integration of the solid of revolution.

Integration 5 (2 hrs):

Integrals that cannot be computed analytically; numerical integration (trapezium and Simpson rules); analysis of the errors.

Complex numbers 1 (2 hrs):

Definition of complex numbers; the imaginary unit; the fundamental theorem of algebra; Adding and multiplying complex numbers; the complex conjugate; dividing complex numbers.

Complex numbers 2 (2 hrs):

Polar representation; De Moivre's formula; complex exponential; Euler's formula; links to the circular functions.

Learning Objectives

On completion of this module a learner should be able to:

* Recognize and manipulate an appropriate range of mathematical tools required in chemistry and chemical engineering.

* Demonstrate the application of mathematics to solve routine chemistry and chemical engineering problems.

* Model simple chemistry and chemical engineering processes.

In particular, students will be able to solve problems involving:

§ Polynomials and elementary functions
§ Cartesian representation of functions
§ Numerical solution of nonlinear equations
§ Differentiation and its applications
§ Integration and its applications
§ Complex numbers

Skills

Learners are expected to demonstrate the following on completion of the module:

* Students will grow their confidence in identifying and applying mathematical tools required to progress their studies in either chemistry or chemical engineering. During the module, students will practice:

* Logical thinking

* Critical assessment of a mathematical derivation

* Independent and group learning

Assessment

Assessment Profile
Element type Element weight (%)
1. One differentiation test (CANVAS) 50
2. One Integration test (CANVAS) 50

Course Requirements:
Class test at 40 %
Assessed Classes Attendance at 80 %
Coursework Mark Veto at 40 %