Mathematical Methods 2 (Adv Stand) (U01696)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-2-mm2A

Separable differential equations, linear differential equations with constant coefficients. Partial differentiation, implicit differentiation, directional derivative, higher derivatives and the chain rule. Arithmetic and geometric series, binomial theorem. Functions, limits, special cases, L'Hopital's rule. Power series, radius of convergence, Maclaurin and Taylor series, error estimates. Hyperbolic functions and their inverses, differentiation and integration. Integration: integration by parts and substitution methods, arc-lengths and areas.

Entry Requirements

? Pre-requisites : AH-grade Mathematics or equivalent

? Prohibited combinations : MAT-1-mi2, MAT-1-mm2

? Special Arrangements for Entry : This course and its companion "Applicable Mathematics 2 (Adv Stand)" are usually taken together; the sessions listed under "Scheduled Class Hours" often cover both. The entries that feed into Timetab must be distinct, to avoid a clash, so they do not show the true timetable.

Subject Areas

Home subject area

Other Non-Specialist courses (School of Mathematics), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
18/09/2007	14:00	16:00			Lecture Room 5326, JCMB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Lecture	Tuesday	14:00	15:50	KB
Lecture	Thursday	14:00	15:50	KB

? Additional Class Information : Lectures: shared with MAT-2-am2A

Summary of Intended Learning Outcomes

Differential Equations
1. Ability to identify and solve separable differential equations
2. Ability to solve linear homogeneous differential equations of order one with constant coefficients.
3. Ability to find particular solutions for linear inhomogeneous differential equations of order one with constant coefficients.
4. Ability to fit initial conditions.

Further Differentiation
1. Ability to calculate simple partial derivatives.
2. Ability to differentiate implicit functions.
3. Ability to calculate directional derivatives.

Special Sequences and Series
1. Ability to identify and sum arithmetic and geometric series.
2. Ability to use the binomial theorem.

Limits
1. Understanding concept of functions.
2. Knowledge of limits of combinations of log, polynomial and exponential functions.
3. Ability to use L'Hopital's Rule.

Series
1. Understanding the nature of power series and the radius of convergence.
2. Ability to undertake simple calculations using the geometric, binomial, exponential and trigonometric series.
3. Ability to construct Maclaurin and Taylor series.

Functions and Integration
1. Ability to work with elementary transcendental functions, especially hyperbolic functions and their inverses.
2. Ability to evaluate integrals in terms of inverse circular functions.
3. Ability to use integration by parts.
4. Ability to use substitutions of various types.
5. Ability to calculate arc- lengths and areas for parametric functions.