Undergraduate Course: Mathematical Methods 2 (MATH08032)
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.*
Hyperbolic functions, inverse trigonometric functions. Differentiation of inverse functions and its use in integration. Integration by parts. Separable differential equations. First order linear differential equations with constant coefficients. Direction fields, Euler's method, trapezium and Simpson's rule with extrapolation, Newton-Raphson method. Implicit, parametric and polar functions. Introduction to partial differentiation, directional derivative, differentiation following the motion, differentials and implicit functions. Limits and improper integrals, substitution. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
Further function types: understanding
1. the definition and properties of hyperbolic functions
2. the definition and properties of inverse trigonometric functions and using them to solve trigonometric problems
3. implicit functions and ability to graph them
4. parametric functions and ability to graph them
5. how to translate between cartesian and polar coordinates and draw simple polar curves
Further Differentiation: ability
1. to understand inverse functions and to differentiate hose for sin and tan
2. to use hyperbolic functions, including simple calculus properties
3. to differentiate implicit functions
4. to calculate simple partial derivatives
5. to calculate directional derivatives
6. of perform differentiation following the motion
7. to construct and use differential expressions
8. to use Newton-Raphson's method
9. to understand the notation used in thermodynamics
Further Integration: ability
1. to evaluate integrals in terms of inverse circular functions
2. to use integration by parts
3. to use substitutions of various types
4. to calculate arc-lengths and areas for parametric functions
Differential equations: ability
1. to identify and solve separable differential equations
2. to solve linear homogeneous first-order differential equations with constant coefficients
3. to find particular solutions for linear differential equations with constant coefficients, for simple right-hand sides
4. to fit initial and boundary conditions
Numerical calculus: ability
1. to use the composite trapezium rule
2. to use Simpson's rule
3. to apply Richardson's Extrapolation to trapezium and Simpson's rules
4. to draw direction fields and sketch solution curves
5. to use Euler's Method for differential equations
Limits and Continuity: ability
1. to use L'Hopital's Rule
2. to use the limits of combinations of log, polynomial and exponential functions
3. to evaluate 'improper' integrals |
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 | mm2 |
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 |
|
|
University Homepage