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NST Part IA EMB Synopsis

Algebra, Units and Graphs (4 lectures)

Numbers, basic operations, algebra as a language for expressing relations between numbers or physical quantities.

Solving equations

Rearranging equations

Quadratic equations

Simultaneous equations

Equations involving units

Physical quantities expressed as numbers with units

Change of units

Amounts and concentrations

Preparation of solutions

 

Trigonometry, oscillations and waves (3 lectures)

Plotting graphs of equations: functions, gradients, redefining variables

Trig. Functions sin, cos, tan, inverse functions

Simple harmonic motion

Basic properties of propagating waves

 

Logarithms and raising to powers (2 lectures)


Calculus (11 lectures)

Differentiation

Relation to slope or gradient of a curve

Use of formulae for powers, elementary functions etc.

Chain rule

Turning points, maxima and minima

Integration, indefinite and definite

Inverse of differentiation

Relation to summation

Relation to area under the curve

Change of variable

ln(x) as the integral of 1/x

Relation of ln(x) and log(x)

Exponential and trig functions

First order differential equations

e.g. dy/dx = ky

 

Statistics (10 lectures)

Presenting data, histograms

Mean, Mode and Median

Samples and populations

Basic probability using a binomial variable

Additive and multiplicative properties of probabilities, conditional probabilities

Variance, SD and SE

The normal distribution, t and z distributions

Confidence intervals

Significance testing, the t-test

Chi-squared test

 

Curve Fitting (4 lectures)

Linear regression

Theory

Practical calculations

Limitations

Non-linear least squares curve fitting using Excel

Limitations of Excel's Solver