Math General Flashcards by Om Sikaria

Mechanics Modelling assumptions

Smooth pulley
Light pulley
Inextensible string
Particle
Rod
Smooth / Rough surface

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Mechanics Modelling assumptions- Smooth pulley

Tension on either side of the pulley is equal

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Mechanics Modelling assumptions - light string

Tension is equal throughout the string

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Mechanics Modelling assumptions - inextensible string

Both particles have the same acceleration

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Mechanics Modelling assumptions - particle

Ignore air resistance, Ignore rotational effects

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Mechanics Modelling assumptions - Rod

Means that it is rigid (doesn’t bend) and has no thickness

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CP1 - 9 - converting vector to Cartesian equation of a plane

Dot each direction vector in plane with xyz = 0 to form 2 simultaneous equations and let a=1 and solve them for normal vector xyz

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CP1 - 9 - Finding angle between 2 lines

Use dot product on the direction of each of the lines

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CP1 - 9 - Finding angle between line and plane

Use dot product on the direction of the line and the normal to the plane. Subtract the angle found from 90.

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CP1 - 9 - Finding angle between 2 planes

Use dot product on the direction of the normals of each of the planes

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CP1 - 9 - Finding POI between 2 lines

Set the general point on both line equal to a point (x,y,z) and solve for lambda and mu and for x,y,z to find POI

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CP1 - 9 - Finding POI between line and plane

Sub in general point on line into Cartesian equation of plane and find value of mu and poi.

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CP1 - 9 - Finding POI between 2 planes

Find 2 common points on both planes and find the vector through them and form line equation.

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CP1 - 9 - Finding shortest distance between 2 skew lines

Find general point on L1 & L2
Find vector between them
Ensure this is perp to L1 & L2

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CP1 - 9 - Finding shortest distance between 2 parallel lines

Find general point on L1 & L2
Find vector between them - use t = mu - lambda
Ensure this is perp to L1

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CP1 - 9 - Finding shortest distance between a point and a plane

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CP1 - 9 - reflecting a point in a plane

Find equation of line through point and closest point on the plane using coordinates of point and Normal to plane.
Put general line eqn in plane eqn to find value for lambda. Double value of lambda and sub into line eqn to find reflected point.

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CP1 - 9 - reflecting a line in a plane

Find POI
Reflect a point on the line in the plane
Find the eqn of the line through these 2 points

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Inverse of 2x2 matrix

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Determinant and inverse of a 3x3 matrix

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Planes meeting at single point

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Sheaf

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Prism

After eliminating variables the 2 equations are inconsistent
Ax+by=c
Ax+by=d

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Parallel and non identical planes

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3 same planes

Matricies invariant points, line, line of invariant points

Invariant points - Points that don’t move under a transformation Line of Invariant points - line of Points that don’t move under a transformation Invariant ine - any line whereby any point on it is transformed to a point on the same line is called an invariant line

General 2x2 anticlockwise rotation matrix

Cos, -sin Sin, Cos

3D rotation about xaxis matrix

3D rotation about y-axis matrix

3D rotation about z-axis matrix

Roots of polynomials formulas

Sums of n, n^2, n^3

Summation induction

Divisibility induction

Matricies induction

Roots of polynomials (alpha + beta + gamma)^2/3

DRV - E(x), Var(x)

Poisson distribution

Binomial mean and variance and poisson approximation requirements

Geometric distribution

Negative binomial

Variance

Coding - mean and standard deviation

Median and quartile

For non grouped data do n+1 but for grouped data do just n and do linear interpolation

Probability set notation

For mutually exclusive events P(A or B)

Probability set notation

For independent events P(A and B)

For non mutually exclusive events P(A or B)

Conditional probability

PMCC hyp test - 1 tailed reject general

PMCC hyp test - 1 tailed success general

PMCC hyp test - 2 tailed initial general

Cumulative frequency curves

Use upper class boundaries with cumulative frequencies

Frequency polygon

Use middle of class boundary and regular frequency

Histogram

Frequency density = frequency / class width Area = K * Frequency

poisson hyp test

Poisson as binomial approx hypothesis test

Poisson hypothesis test critical region and actual significance level

Set notation pure

When solving an equation what to do when squaring both sides

Check if solutions work

Concave

Second derivative is negative

Convex

Second derivative is positive

Transformations

Unit vector

Binomial expansion formula for (1+x)^n

Parametric differentiation

Parametric integration

Newton ralphson method formula

Iteration - numerical method

Iteration - convergence condition

Area enclosed by a polar curve

Polar differentiation

% of data within 1/2/3 standard deviations from the mean of normal distribution

68/95/99.7

Normal distribution - sample mean

Central limit theorem

Normal distribution - sample mean

Goodness of fit chi squared formula

Combine sections with a contribution less than 5

Degrees of freedom - chi squared

Chi squared - contingency table

Elastic strings and springs

Maclaurin series for e^x

Maclaurin series for ln (1+x)

converges for -1

Maclaurin series for sin(x)

Maclaurin series for cos(x)

derivative of tan x

sec^2(x)

derivative of cosec x

-cosec x cot x

derivative of cot x

-cosec^2 x

derivative of sec x

sec x tan x

integral of tan kx

integral of cot kx

integral of cosec kx

integral of sec kx

integral of sec^2 kx

derivative of sinhx, coshx, tanhx

derivative of arcsinhx

derivative of arcoshx

derivative of arctanhx

integral of tanhx

derivative of sech x

−sech x tanh x

derivative of coth x

derivative of cosech x

-cosech(x)cot(x)

hyperbolic trig identities pythag trig equivalent

hyperbolic double angle trig identities

hyperbolic compound angle trig identities

Inverse hyperbolic functions graphs

Mclaurin series

Nth roots of a complex number z=re^itheta

General form for roots of unity

For a probability generating function how do you find E(x), Var(x)

If X and Y are two independent random variables with probability generating function Gx(t) and Gy(t), the probability generating function of Z = X + Y is given by:

If the discrete random variable X has probability generating function Gx(t), then the probability generating function of the discrete random variable Y = aX + b, where a and b are positive integers, is given by

quality of tests - size and power, type 1, type 2

Math General Flashcards

(119 cards)