F1 Chapter 1 - Introduction to complex numbers
F1 Chapter 1 - Introduction to complex numbers
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F1 1.1 Complex numbers
F1 1.1 Complex numbers
Cardano's search for a formula to solve cubic equations led to the discovery of complex numbers.
Watch video - Cardano's Formula here ...... - PDF notes here ......
F1 1.2 The maths behind why Cardano's formula for a cubic did not always work.
F1 1.2 The maths behind why Cardano's formula for a cubic did not always work.
Watch video here ...... PDF notes here ......
F1 1.3 Complex numbers - basic rules
F1 1.3 Complex numbers - basic rules
Watch video here ...... PDF notes here ......
F1 1.4 Argand Diagram - complex numbers on a plane.
F1 1.4 Argand Diagram - complex numbers on a plane.
Watch video here ...... PDF notes here ......
F1 1.5 Modulus-argument form
F1 1.5 Modulus-argument form
Watch video here ...... PDF notes here ......
F1 1.6 Equality of complex numbers and finding square roots
F1 1.6 Equality of complex numbers and finding square roots
Watch video here ...... PDF notes here ......
F1 1.7 Complex roots of polynomial equations
F1 1.7 Complex roots of polynomial equations
Watch video here ...... PDF notes here ......
Those who want to see a proof that roots of a polynomial equation with real coefficients occur in conjugate pairs should read the PDF notes here ......
Those who want to see a proof that roots of a polynomial equation with real coefficients occur in conjugate pairs should read the PDF notes here ......
F1 Chapter 2 - Roots of polynomial equations
F1 Chapter 2 - Roots of polynomial equations
F1 2.1 Roots of quadratic equations
F1 2.1 Roots of quadratic equations
Watch video here ...... PDF notes here ......
F1 2.1 Roots of cubic and quartic equations
F1 2.1 Roots of cubic and quartic equations
Watch video here ...... PDF notes here ......
F1 Chapter 3 - Numerical solutions of equations
F1 Chapter 3 - Numerical solutions of equations
F1 3.1 Interval bisection
F1 3.1 Interval bisection
Watch video here ...... PDF notes here ......
F1 3.2 Linear Interpolation
F1 3.2 Linear Interpolation
Watch video here ...... PDF notes here ......
F1 3.3 Newton Raphson
F1 3.3 Newton Raphson
Watch video here ...... PDF notes here ......
F1 Chapter 4 - Coordinate systems
F1 Chapter 4 - Coordinate systems
F1 4.1 Parametric equations for parabolas and rectangular hyperbolas
F1 4.1 Parametric equations for parabolas and rectangular hyperbolas
Watch video here ......
F1 4.2 Focus and directrix
F1 4.2 Focus and directrix
Watch video here ...... PDF notes for parametric eqns and focus and directrix here ......
F1 4.3 Tangent and normal at specific point
F1 4.3 Tangent and normal at specific point
Watch video here ...... PDF notes here ......
F1 4.4 Tangent and normal using parametric equations
F1 4.4 Tangent and normal using parametric equations
Watch video here ...... PDF notes here ......
F1 Chapter 5 - Matrix Algebra
F1 Chapter 5 - Matrix Algebra
F1 5.1, 5.2 Basic rules of matrices
F1 5.1, 5.2 Basic rules of matrices
Watch video 5.1 here ......
F1 5.3 Inverse and determinant
F1 5.3 Inverse and determinant
Watch video here ...... PDF notes here ......
F1 5.4 Using inverse matrices to solve equations (easy - no video or notes!)
F1 5.4 Using inverse matrices to solve equations (easy - no video or notes!)
Read pages 103 - 104
F1 Chapter 6 - Transformations using matrices
F1 Chapter 6 - Transformations using matrices
F1 6.1 Matrix transformations
F1 6.1 Matrix transformations
Watch video 6.1 here ...... PDF notes F1 6.1 Linear transformations here ......
F1 6.2 Base vectors and transformations
F1 6.2 Base vectors and transformations
The idea of base vectors is the most important idea in this chapter and you should make sure that you do actually understand the significance of base vectors.
Watch videos 4.3a here ...... and 4.3b here ...... PDF notes here ......
Those who want to know more about the maths behind 'linear' transformations should watch this video here ......
F1 6.3 Combining transformations
F1 6.3 Combining transformations
Watch video here ...... PDF notes here ......
F1 6.4 Inverse and determinant
F1 6.4 Inverse and determinant
Watch video here ...... PDF notes here ......
F1 6.5 Determinant and area,
F1 6.5 Determinant and area,
Watch video here ...... PDF notes here ......
F1 Chapter 7 - Series and sigma notation
F1 Chapter 7 - Series and sigma notation
F1 7.1 Series, Sigma notation
F1 7.1 Series, Sigma notation
Watch video here ...... PDF notes here ......
F1 7.2 Standard Series
F1 7.2 Standard Series
Watch video here ...... PDF notes here ......
F1 Chapter 8 - Proof by induction
F1 Chapter 8 - Proof by induction
F1 8.1 Proof by induction - summation
F1 8.1 Proof by induction - summation
Watch video here ...... PDF notes here ......
F1 8.2 Proof by induction - divisibility problems
F1 8.2 Proof by induction - divisibility problems
Watch videos F1 6.2a here ...... and F1 6.2b here ...... PDF notes here ......
F1 8.3 Proof by induction - recurrence relations
F1 8.3 Proof by induction - recurrence relations
Watch video here ...... PDF notes here ......
F1 8.4 Proof by induction - powers of matrices
F1 8.4 Proof by induction - powers of matrices
Watch video here ...... PDF notes here ......
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