Mathematical Methods 1 (U01679)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-1-mm1

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.

Entry Requirements

? Pre-requisites : H-grade Mathematics or equivalent

? Prohibited combinations : MAT-1-mi1, MAT-1-PCa, MAT-1-mf1

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 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
21/09/2006	09:00	09:50	Lecture Theatre 4, Appleton Tower	Central	Engineers (0900), others (1210)

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-am1)

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