Module Title: | Mathematics 1 |
Language of Instruction: | English |
Module Delivered In |
No Programmes
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Teaching & Learning Strategies: |
This module will be delivered using a mixture of lectures and tutorials.
The Institute Managed Learning Environment will be used to interactively communicate with students e.g. tutorial sheets, on-line tests, discussion forums, reference information.
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Module Aim: |
To give the students the knowledge, competencies and skills necessary to support the mathematical procedures encountered in the other modules of this programme. |
Learning Outcomes |
On successful completion of this module the learner should be able to: |
LO1 |
Apply fundamental algebra theory to solve different types of problems, equations and formulae. |
LO2 |
Produce and interpret graphs; analyse various mathematical functions. |
LO3 |
Prove trigonometric identities and solve triangles. |
LO4 |
Solve problems using complex numbers and apply De Moivre’s theorem. |
LO5 |
Apply appropriate rules and methods to differentiate various functions and solve calculus problems. |
Pre-requisite learning |
Module Recommendations
This is prior learning (or a practical skill) that is recommended before enrolment in this module.
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No recommendations listed |
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. |
No incompatible modules listed |
Co-requisite Modules
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No Co-requisite modules listed |
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. |
No requirements listed |
Module Content & Assessment
Indicative Content |
Basic Algebra
• Apply rules of precedence in calculation
• Use calculator
• Apply rules of indices
• Convert units and use prefixes
• Add, subtract, multiply fractions and algebraic expressions
• Factorise algebraic expressions
• Solve simple equations, simultaneous and quadratic equations
• Transpose formulae
• Use log laws and solve log and exponential equations
• Form Partial Fractions
• Convert between the following number bases: decimal, binary, octal, hexadecimal
• Represent negative numbers in the binary system
• Use and apply permutations and combinations.
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Graphs and Functions
• Plot and note properties of straight line and quadratic graphs
• Plot and note properties of log and exponential graphs
• Prove laws using linear graphs
• Use and apply graphs in engineering applications.
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Trigonometry and Waveforms
• Solve right-angled triangles using Pythagoras’ theorem, trigonometric ratios sine, tangent and cosine and the inverse trigonometric functions
• Use the sine and cosine rules in the solution of non-right angled triangles
• Use degree and radian measure
• Verify trigonometric identities involving all six trigonometric ratios, compound angle formulae and sums and products of sines and cosines
• Apply identities e.g. electrical principles and communications
• Sketch graphs of waves including amplitude, period, frequency, phase angle, wave addition
• Use wave theory and apply it to electrical/electronic principles and mechanics.
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Complex Numbers
• Represent complex numbers in Cartesian and polar form
• Convert from one form to the other
• Understand phasors
• Add, subtract, multiply and divide complex numbers in Cartesian form
• Multiply and divide complex numbers in polar
• Use De Moivre’s Theorem for powers and roots of complex numbers.
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Differential Calculus
• Evaluate simple limits
• Differentiate simple polynomial functions from first principles
• Differentiate by rule algebraic, trigonometric, exponential and logarithmic functions using chain, product and quotient rules
• Apply the derivative as a rate of change and as the slope of the tangent to a curve.
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Assessment Breakdown | % |
Continuous Assessment | 30.00% |
End of Module Formal Examination | 70.00% |
Continuous Assessment |
Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
Other |
Each student will be obliged to complete a continuous assessment programme for which 30% will be awarded. This will involve class tests and other assigned tasks. |
1,2,3,4,5 |
30.00 |
n/a |
End of Module Formal Examination |
Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
Formal Exam |
Each student will sit a formal written examination at the end of the module for which 70% will be awarded. |
1,2,3,4,5 |
70.00 |
End-of-Semester |
SETU Carlow Campus reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time |
Workload Type |
Frequency |
Average Weekly Learner Workload |
Lecture |
Every Week |
3.00 |
Independent Learning |
Every Week |
3.00 |
Tutorial |
Every Week |
1.00 |
Total Hours |
7.00 |
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