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 201112, 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, NewtonRaphson 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
Prerequisites  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 NewtonRaphson'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 arclengths and areas for parametric functions
Differential equations: ability
1. to identify and solve separable differential equations
2. to solve linear homogeneous firstorder differential equations with constant coefficients
3. to find particular solutions for linear differential equations with constant coefficients, for simple righthand 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 

