Mathematical Methods 2 (U01682)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-1-mm2

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.

Entry Requirements

? Pre-requisites : Prior attendance at MAT-1-mm1

? Prohibited combinations : MAT-1-mi2, MAT-2-mm2A

Subject Areas

Home subject area

Mathematics for Physical Science & Engineering, (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 1st year

? Delivery Period : Semester 2 (Blocks 3-4)

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

1 of the following 2 classes

Type	Day	Start	End	Area
Lecture	Mo	09:00	09:50	Central
Lecture	Mo	12:10	13:00	Central

1 of the following 2 classes

Type	Day	Start	End	Area
Lecture	Th	09:00	09:50	Central
Lecture	Th	12:10	13:00	Central

? Additional Class Information : Lectures: M, Th 0900 or 1210
Tutorials: W at 0900, 1000, 1110 or 1210 (shared with MAT-1-am2)

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