Newton-Raphson Method NEW!!
Convergent and Divergent Integrals
Equation of the directrix and coordinates of the focus
Exam Questions – Trig Type
Exam Questions – Matrix transformations
Exam Questions – Newton-Raphson
Exam Questions – Linear Interpolation
Step by step methods
Roots of a quadratic equation
Graphs of rational functions
Tangents and normals to an ellipse
The Ellipse – Cartesian and parametric forms
Relationships between the roots and coefficients of a quadratic equation
Exam Questions – Matrix proofs
Square roots of a complex number
Exam Questions – Series
Exam Questions – Identity and inverse of a 2×2 matrix
Exam Questions – Hyperbola (rectangular)
Exam Questions – Parabola
Exam Questions – Bisection Method
Fractional inequalities
Using known formulae to sum more complex series
Sum of the cubes of the first n natural numbers ∑r3
Sum of the squares of the first n natural numbers ∑r2
Determinant as the area scale factor of a transformation
Inverse matrices to reverse linear transformations
Combinations of transformations
How well do you know your transformations?
Linear transformations – enlargement
Linear transformations – reflections
Linear transformations – rotations
Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
Identity and Inverse of a 2×2 matrix
Matrix multiplication
Addition and subtraction and multiplying a matrix by a scalar
Introduction and dimension of a matrix
Tangents and normals: parametric type
Tangents and normals : Cartesian type
Cartesian and parametric type
Tangents and normals: parametric types
Tangents and normals: Cartesian types
Parabola parametric form
Coordinate geometry: Parabola directrix, focus, locus and equation
Newton-Raphson method for locating a root in a given interval
Linear interpolation method for locating a root in a given interval
The linear interpolation method for locating a root in a given interval is a simple extension to the change of sign method. The following video example demonstrates this method. Example: Find an approximation to the root of x3 + 2x – 2 = 0 using linear interpolation twice over, given that the root lies between 0 and […]
Bisection method for locating a root in a given interval
The bisection method is a simple extension to the change of sign method where an interval in which a root lies is continually bisected (cut in half) until the root is found to the required degree of accuracy. The following example is used to demonstrate this: Example: Find the root of to 1 decimal place […]
Solving problems with complex numbers
Addition, subtraction and multiplying complex numbers and simplifying powers of i
Real and imaginary numbers
Infinite integrals
In this tutorial I show you how to handle integrals where a limit is infinite as in the example below. Example: