Undergraduate Course: Mathematical Methods 1 (MATH08029)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 1 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Mathematics for Physical Science & Engineering |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | *In 2011-12, this course is available only to students retaking it and will be assessed on an 'exam only' basis.*
Functions, graphs, periodicity, special functions. Basic differentiation: rate of change, simple derivatives, rules of differentiation, maxima/minima. Basic integration: anti-derivatives, definite and indefinite integrals. Calculus of exponential, logarithm and trigonometric functions. Rearrangement (trigonometric identities, partial fractions), substitution. Area, arc-length, volume, mean values, rms values and other summation applications of integration. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
Functions
1. Understanding concept of functions, including piecewise ones
2. Ability to graph functions, using appropriate calculus techniques
3.Understanding periodicity, evenness and oddness and using it to solve computational and graphical problems
4. Ability to graph f(ax+b), given the graph of f(x)
5. Ability to evaluate and graph piecewise functions
Differentiation
1. Understanding and application of derivative as a rate of change; understanding its graphical interpretation
2. Ability to differentiate polynomials in standard form and all powers of x, including higher derivatives
3. Ability to use the product, quotient and chain rules
4. Ability to use differentiation to solve optimisation problems
Integration
1. Ability to evaluate an integral by anti-differentiation
2. Understanding an integral as a sum
3. Ability to integrate polynomials in standard form and all powers of x
4. Ability to use simple rearrangements (trigonometric and partial fractions) and simple substitution
5. Ability to construct integrals using the summation definition, with applications
Trigonometric functions
1. Ability to evaluate all six ratios from given information
2. Ability to use addition formulae and multiple angle-formulae, including their reversals
3. Ability to calculate amplitude, period and phase for sinusoidal functions
4. Ability to differentiate and integrate sin, cos, tan
5. Ability to integrate squares and products of sin and cos
Logarithms and Exponentials
1. Understanding the definition of a log as the inverse of exponentiation and ability to solve simple problems using this
2. Ability to manipulate exponential functions
3. Ability to use the log rules
4. Ability to differentiate ln x
5. Ability to integrate 1/(ax+b) and f'/f; ability to differentiate and integrate ekx
6. Ability to use log-linear and log-log graphs, including understanding of exponential processes
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Assessment Information
Coursework: 15%
Degree Examination: 85% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | mm1 |
Contacts
| Course organiser | Dr Noel Smyth
Tel: (0131 6)50 5080
Email: N.Smyth@ed.ac.uk |
Course secretary | Ms Marieke Blair
Tel: (0131 6)50 5048
Email: M.Blair@ed.ac.uk |
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