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Keeganmaths
United Kingdom
Приєднався 15 лют 2016
This Channel holds demonstration videos for A Level Questions. They cover the Edexcel 2017 Maths Syllabus.
There are Playlists covering: Statistics, Mechanics and Pure topics, for both A Level and Further Maths.
There are also Playlists for the old MEI and AQA Syllabus.
There are Playlists covering: Statistics, Mechanics and Pure topics, for both A Level and Further Maths.
There are also Playlists for the old MEI and AQA Syllabus.
CENTRAL LIMIT THEOREM
This video presents the Central Limit Theorem using an online simulator.
It shows that if sample size is N greater than 25/30 for an parent distribution, the Sample Mean is Normally distributed. This means that normal distribution probabilities can be used for calculations and Hypothesis Testing.
Online simulator:
onlinestatbook.com/stat_sim/sampling_dist/index.html
It shows that if sample size is N greater than 25/30 for an parent distribution, the Sample Mean is Normally distributed. This means that normal distribution probabilities can be used for calculations and Hypothesis Testing.
Online simulator:
onlinestatbook.com/stat_sim/sampling_dist/index.html
Переглядів: 51
Відео
REGRESSION LINES - LEAST SQUARES PROOF
Переглядів 2,5 тис.2 роки тому
This video explains the concept of Least Squares regression. It provides a full proof of the Regression Line Formula. It derives the Total Error as the sum of the squares of the residuals. It shows the minimising of the Total Error with respect to a and b. It solves the simultaneous equations.
MARKOV CHAINS - Equilibrium Probabilities
Переглядів 3,8 тис.3 роки тому
This video investigates the long-term probabilities created by Markov Chains - represented by Probability based Transition Matrices. It demonstrates that there are Equilibrium Probabilities towards which probabilities converge. These Equilibrium Probabilities represent the Invariant Points of the Matrix. Convergence is demonstrated using Invariant Line analysis. This video goes beyond the Furth...
MARKOV CHAINS - Introduction
Переглядів 1183 роки тому
This video introduces Markov Chains - Transition Matrices using Conditional Probabilities used to predict future events. The example used is whether tomorrow will be Fine or Wet using conditional probabilities based on whether today is Fine or Wet. The example shows the solution using a Probability Tree, and then converts the method to Matrices.
TRANSITION MATRICES - Long-term Trends and Invariant Lines
Переглядів 1,2 тис.3 роки тому
This video investigates long-term populations over time for different initial conditions. The example investigates the Adult and Juvenile Population over 1, 10 and 100 years. The initial population ratio is varied Adult:Juvenile, to show that the long-term ratio is independent of the initial ratio. The investigation shows that the long-term ratio follows the dominant Invariant Line for the Tran...
TRANSITION MATRICES - Introduction
Переглядів 603 роки тому
This video introduces Transitionary Matrices. The predict future populations from initial populations. This video predicts the population of Adult and Juvenile Meerkats 'year on year' from an initial population. This is a popular Further Maths topic.
MATRIX TRANSFORMATIONS - INVARIANT LINES
Переглядів 2553 роки тому
This video shows how to find Invariant Lines using Mx = λx. The video finds the Invariant Lines for Stretches, Rotations and Reflections - and the special cases.
MATRIX TRANSFORMATIONS - INVARIANT POINTS
Переглядів 1283 роки тому
This video demonstrates how to find Invariant Point from 2x2 matrix equation: Mx = x. The video finds the invariants points for general stretches, rotations and reflections - along with the special cases.
MATRICES - GENERAL REFLECTION MATRIX
Переглядів 5373 роки тому
This video deduces the general form of the reflection matrix. This is in terms of the angle the Lines of Reflection (mirror line) is from the horizontal axis.
MATRICES - COMBINING DIFFERENT TYPES OF TRANSFORMATIONS
Переглядів 153 роки тому
This video proves the general solutions for combinations of: -Reflection then Rotation. -Rotation the Reflection. These both result in Reflections - but the reflection angles are different.
MATRICES - COMBINING SAME TYPE OF TRANSFORMATIONS
Переглядів 293 роки тому
This video finds the general results to combining the same transformations: stretch stretch, rotation rotation, reflection reflection. Remember: transformation matrices operate right to left - as the vector will be on the right.
EULER'S METHOD - 2nd Order Differential Equations
Переглядів 11 тис.3 роки тому
This video demonstrates using Euler's Method to create a numerical approximate solution for a 2nd Order Differential Equations. The method uses a Quadratic Fit to predict the next point - using the 2nd Differential from the Diff Eqn. The video demonstrates improving the accuracy of the results by reducing the size of the increment (increasing the number of iterations).
MID-POINT METHOD - 1st Order Differential Equations
Переглядів 1,8 тис.3 роки тому
The video demonstrates how to use the Mid-Point method to find a numerical approximate solution to a 1st Order Differential Equation. It demonstrates that this method is more accurate than the Euler Method.
EULER'S METHOD - 1st Order Differential Equations
Переглядів 1,2 тис.3 роки тому
This video demonstrates Euler's method of finding a numerical approximation to a 1st Order Differential Equation. It demonstrates improvement by reducing the interval.
L'HOPITAL'S RULE
Переглядів 93 роки тому
Video proving and using L'Hopital's Rule to find the limit of Division of Function f/g at x=a, where the values result in 0/0 or infinity/infinity - using the division of the Differentials. Two examples to demonstrate for sine/x and lnx/1/x. Extension shown where the gradients are also 0 such that 0/0 - then use the 2nd Differential. Note: method repeats for 0/0 to nth differentials.
LIMITS - Solving for 0/0 (using Taylor Series)
Переглядів 3133 роки тому
LIMITS - Solving for 0/0 (using Taylor Series)
DIFFERENTIAL EQUATIONS - APPROXIMATE SOLUTION WITH TAYLOR SERIES
Переглядів 5043 роки тому
DIFFERENTIAL EQUATIONS - APPROXIMATE SOLUTION WITH TAYLOR SERIES
DIFFERENTIAL EQUATIONS - 2ND ORDER - REDUCE DIFFERENT DEGREES
Переглядів 673 роки тому
DIFFERENTIAL EQUATIONS - 2ND ORDER - REDUCE DIFFERENT DEGREES
DIFFERENTIAL EQNS - 2ND ORDER - REDUCE SAME DEGREE
Переглядів 143 роки тому
DIFFERENTIAL EQNS - 2ND ORDER - REDUCE SAME DEGREE
DIFFERENTIAL EQNS 1ST ORDER - REDUCING BERNOULLI EQUATIONS
Переглядів 163 роки тому
DIFFERENTIAL EQNS 1ST ORDER - REDUCING BERNOULLI EQUATIONS
DIFFERENTIAL EQNS 1ST ORDER - REDUCING MIXED EQUATIONS
Переглядів 313 роки тому
DIFFERENTIAL EQNS 1ST ORDER - REDUCING MIXED EQUATIONS
DIFFERENTIAL EQUATIONS 2ND ORDER - RESONANCE
Переглядів 8913 роки тому
DIFFERENTIAL EQUATIONS 2ND ORDER - RESONANCE
DIFFERENTIAL EQUATIONS 2ND ORDER - DAMPING
Переглядів 6963 роки тому
DIFFERENTIAL EQUATIONS 2ND ORDER - DAMPING
NEGATIVE BINOMIAL DISTRIBUTION - PART 2
Переглядів 263 роки тому
NEGATIVE BINOMIAL DISTRIBUTION - PART 2
NEGATIVE BINOMIAL DISTRIBUTION - PART 1
Переглядів 283 роки тому
NEGATIVE BINOMIAL DISTRIBUTION - PART 1
SYSTEMS OF DIFFERENTIAL EQUATIONS - REAL-LIFE APPLICATIONS
Переглядів 1,4 тис.3 роки тому
SYSTEMS OF DIFFERENTIAL EQUATIONS - REAL-LIFE APPLICATIONS