| Title: | Maths for Physical Sciences |
|---|
| Long Title: | Maths for Physical Sciences |
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| Field of Study: |
Mathematics
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| Valid From: |
Semester 1 - 2018/19 ( September 2018 ) |
| Next Review Date: |
March 2023 |
| Module Coordinator: |
David Goulding |
| Module Author: |
HANNAH LORDAN |
| Module Description: |
An introduction to fundamental mathematical calculations and problem solving aimed at consolidating and developing student competence in the mathematical techniques which are central to the Physical Sciences. |
| Learning Outcomes |
| On successful completion of this module the learner will be able to: |
| LO1 |
Perform a range of arithmetical calculations necessary for laboratory work in the Physical Sciences. |
| LO2 |
Manipulate a wide variety of algebraic expressions, transpose formulae, solve linear and quadratic equations and solve systems of simultaneous equations. |
| LO3 |
Use the laws of indices and logarithms to solve related equations arising in applied problems. |
| LO4 |
Sketch graphs relating to quantities which are: in direct proportion and in inverse proportion; related linearly, exponentially or logarithmically. |
| LO5 |
Reduce equations to linear form and determine parameters from appropriate graphs. |
| LO6 |
Sketch sinusoidal waveforms and identify their salient characteristics. |
| LO7 |
Perform basic algebraic manipulation of complex numbers and know how to represent them in polar, rectangular and exponential forms. |
| Pre-requisite learning |
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). |
|
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. |
| No incompatible modules listed |
Co-requisite Modules
|
| No Co-requisite modules listed |
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
|
| No requirements listed |
Module Content & Assessment
| Indicative Content |
|
The Fundamentals of Arithmetic with Applications
Rounding to significant figures. Scientific and Engineering notation. SI units, prefixes, conversion of units including imperial and metric. Ratio and proportion with examples from the Physical Sciences. Application to molarity and concentration. Approximation, error estimation: absolute, relative and percentage error.
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Basic Algebra
Algebraic manipulation, transposition and simplification of formulae relevant to the Physical Sciences. Solution of linear and quadratic equations. Simultaneous equations with two or three variables.
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Indices and Logarithms
The laws of indices. Logarithms and their use in the solution of indicial (exponential) equations. Discussion of the number e and natural logarithms.
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Functions and Graphs
Function notation with particular emphasis on functions of one variable. Independent variable, dependent variable. Graphs of quantities which are in direct proportion and indirect proportion. Graphs of linear functions and quadratic functions. Exponential growth and exponential decay. Reduction of non-linear relations to linear form to allow for the estimation of parameters.
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Trigonometry.
Angle measurement in degrees and radians. Trigonometric ratios and the unit circle. Pythagoras theorem. Solution of simple trigonometric equations. Graphing sine and cosine waveforms. Characteristics of a waveform: amplitude, period, frequency and phase.
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Complex numbers
Rectangular, polar and exponential forms.
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| Assessment Breakdown | % |
|---|
| Course Work | 40.00% |
| End of Module Formal Examination | 60.00% |
| Course Work |
|---|
| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Short Answer Questions |
In class test |
1,2,3 |
20.0 |
Week 5 |
| Short Answer Questions |
In class test |
4,5,6 |
20.0 |
Week 10 |
| End of Module Formal Examination |
|---|
| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Formal Exam |
End-of-Semester Final Examination |
1,2,3,4,5,6,7 |
60.0 |
End-of-Semester |
| Reassessment Requirement |
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.
|
The institute reserves the right to alter the nature and timings of assessment
Module Workload
| Workload: Full Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Exposition of theory with illustrative concrete examples |
3.0 |
Every Week |
3.00 |
| Tutorial |
Student problem solving under guidance of class tutor |
2.0 |
Every Week |
2.00 |
| Independent & Directed Learning (Non-contact) |
Study of lecture material and exercise sheets |
2.0 |
Every Week |
2.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
5.00 |
| Workload: Part Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Exposition of theory with illustrative concrete examples |
2.0 |
Every Week |
2.00 |
| Tutorial |
Student problem solving under guidance of class tutor |
1.0 |
Every Week |
1.00 |
| Independent & Directed Learning (Non-contact) |
Study of lecture material and exercise sheets |
4.0 |
Every Week |
4.00 |
| Total Hours |
7.00 |
| Total Weekly Learner Workload |
7.00 |
| Total Weekly Contact Hours |
3.00 |
Module Resources
| Recommended Book Resources |
|---|
- John Bird 2017, Basic Engineering Mathematics, 7th Edition, Routledge [ISBN: 978-113867370]
- Stroud, K.A.; Booth, Dexter J. 2009, Foundation Mathematics, Palgrave MacMillan England [ISBN: 9780230579071]
| | Supplementary Book Resources |
|---|
- Alicia Sevilla & Kay Somers 2007, Quantitative Reasoning: Tools for Today's Informed Citizen, First Ed., Key College Publishing USA [ISBN: 878-1-931914-90-1]
- COMAP 2002, For All Practical Purposes: Mathematical Literacy in Today's World, Sixth Ed., COMAP USA [ISBN: 978-0716738176]
- James F. Burkhart 1999, Quantitative and qualitative reasoning skills, Second Ed., Kendall/Hunt Publishing USA [ISBN: 978-0787263782]
- Donald Pierce, Don Pierce & Edward B. Wright 1997, Mathematics for Life: A Foundation Course for Quantitative Literacy, Preliminary Ed., Prentice Hall [ISBN: 978-0134938592]
- Paul Monk and Lindsey J. Munro, Maths for chemistry [ISBN: 978-0-19-954129-4]
- Applying maths in the chemical and biomolecular sciences: an example-based approach [ISBN: 978-0-19-923091-4]
- Philip R. Bevington, D. Keith Robinson, Data reduction and error analysis for the physical sciences [ISBN: 978-0-07-119926-1]
| | Supplementary Article/Paper Resources |
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- Mathematical Association of America 2007, Calculation vs. Context
| | Other Resources |
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- Website: CIT Maths Online
- Website: Franco Vivaldi 2009, Essential Mathematics Web-book
- Website: Eric WeissteinWolfram MathWorld
- Website: Wolfram Alpha
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Module Delivered in
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