Inventory
Workbook 1 – Basic Algebra
 Slide 1
Modulus
 Slide 2
Factorial
 Slides 3 – 4
Summation
 Slides 5 – 10
Indices
 Slide 11
Scientific Notation
 Slide 12
Polynomials
 Slides 13 – 15
Fractions
 Slides 16 – 18
Factorisation
 Slides 19 – 28
Simplification
 Slide 29
Rearranging Formulae
Workbook 2 – Basic Functions
 Slides 1 – 2
Domain and Range
 Slide 3
Identifying a One-to-Many Function
 Slides 4 – 6
Continuous & Discontinuous Functions
 Slide 7 – 8
Even Functions
 Slide 9
Distance Between Points
 Slide 10
Identifying a Cubic Graph
 Slides 11 – 17
Equations of a Straight Line
Workbook 3 – Equations, Inequalities and Partial Fractions
 Slide 1
Substitution
 Slides 2 – 4
Linear Equations
 Slides 5 – 9
Quadratic Equations
 Slides 10 – 15
Polynomials
 Slides 16 – 20
System of Equations
 Slides 21 – 24
Inequalities
 Slides 25 – 27
Partial Fractions
Workbook 4 – Trigonometry
 Slides 1 – 7
Trigonometric Functions
 Slides 8 – 10
Sine and Cosine Rule
 Slide 11
Equivalent Angles
 Slides 12 – 13
Radians
 Slides 14 – 16
Applications of Trigonometry
Workbook 6 – Exponential and Logarithmic Functions
 Slides 1 – 4
Exponential Functions
 Slides 5 – 14
Logarithms
Workbook 7 – Matrices
 Slides 1 – 5
 Slides 6 – 9
 Slides 10 – 17
 Slide 18
 Slide 19
 Slide 20
 Slide 21
 Slides 22 – 23
 Slides 24 – 27
 Slide 28
 Slides 29 – 32
Systems of equations
Inverses
Matrix multiplication
Transpose
Trace
Identity
Symmetric matrices
Addition
Determinants
Upper triangular matrices
Matrix theory
Workbook 9 – Vectors
 Slides 1 – 6
 Slides 7 – 11
 Slides 12 – 17
 Slides 18 – 20
 Slides 21 – 22
 Slides 23 – 24
 Slides 25 – 23
 Slide 27
 Slide 28
 Slides 29 – 30
 Slide 31
 Slides 32 – 33
 Slide 34
Scalar product
Magnitude
Vector product
Solving vectors in perpendicular directions
Vector addition
Position vectors
Unit vectors
Direction ratio
Direction cosines
Normal vectors
Scalars
Vector theory
Vectors joining points
Workbook 10 – Complex Numbers
 Slides 1 – 2
Properties of a Complex Number
 Slides 3 – 4
Defining Real and Imaginary Parts
 Slides 5 – 7
Addition, Multiplication & Division
 Slide 8
Magnitude
 Slide 9
Complex Conjugate
 Slide 10
Complex Roots
 Slide 11
Argand Diagrams
 Slides 12 – 14
Polar Coordinate Form
 Slides 15 – 16
Exponential form
 Slide 17
De Moivre’s Theorem
 Slide 18
Finding complex values of a number
Workbook 11 – Differentiation
 Slides 1 – 2
Limit definition
 Slides 3 – 12
Finding the Derivative
 Slide 13
Differentiation Rules
 Slides 14
Addition Rule
 Slides 15 – 17
Product Rule
 Slides 18 – 20
Quotient Rule
 Slide 21
Chain Rule
 Slide 22
Identifying Which Rule to Use
 Slide 23
Understanding Derivatives
 Slides 24 – 25
Finding the Second Derivative
 Slides 26 – 29
Parametric Differentiation
 Slides 30 – 32
Implicit Differentiation
Workbook 12 – Applications of Differentiation
 Slides 1 – 6
Stationary Points
 Slides 7 – 11
Vector Differentiation
 Slides 12 – 14
Tangents and Normals
 Slide 15
Curvature
Workbook 13 – Integration
 Slides 1 – 11
Indefinite integrals
 Slides 12 – 17
Definite integrals
 Slides 18 - 23
Integration by parts
 Slides 24 – 29
Integration by substitution
 Slides 30 – 31
Integrals which give rise to Logarithms
 Slides 32 – 35
Partial fractions
 Slides 36 – 38
Theory
Workbook 14 – Applications of Integration
 Pages 1 – 3
Volume of revolution
Workbook 15 – Applications of Integration 2
 Slides 1 – 5
Centre of mass
Workbook 16 – Sequences and Series
 Slide 1
Summation
 Slide 2
Sum of a Series
 Slides 3 – 5
Convergent and Divergent Series
 Slide 6
Geometric Series
Workbook 18 – Functions of Several Variables
 Slides 1 – 2
Functions of 2 or More Variables
 Slides 3 – 4
Partial Derivatives
 Slides 5 – 6
Second Partial Derivatives
 Slides 7 – 8
Stationary Points
 Slides 9 – 10
Types of Stationary Points
 Slide 11
Relative Error
 Slides 12 – 13
Absolute Error
 Slide 14
Percentage Relative Error
Workbook 19 – Differential Equations
 Slide 1
Order
 Slides 2 – 5
Using Separation of Variables
 Slide 6 – 7
Using Initial Conditions
 Slides 8 – 9
Trial Solution
 Slides 10 – 14
Exact Equations
 Slides 15 – 16
Integrating Factor
 Slides 17 – 21
Second Order ODEs
 Slides 22 - 23
Complimentary Function
 Slides 24 – 26
Particular Integral
Workbook 20 – Laplace Transforms
 Slide 1
Laplace Transform
 Slides 2 – 4
Casual Functions
 Slide 5
Derivative
 Slide 6
Finding Area of Given Curve
 Slides 7 – 8
Laplace Transforms of Delayed Step Function
 Slide 9
Inverse Laplace Transform using Partial Fractions
 Slide 10
First Shift Theorem
 Slide 11
Inverse Laplace Transforms
Workbook 22 – Eigenvalues and Eigenvectors
 Slides 1 – 2
Determinants
 Slides 3 – 5
System of Equations
 Slides 6 – 8
Properties of Eigenvalues
 Slide 9
Characteristic Equation
 Slides 10 – 14
Finding Eigenvalues
 Slides 15 – 18
Finding Eigenvectors
 Slide 19
Linear Independence
 Slide 20
Normalising an Eigenvector
 Slides 21 – 26
Diagonalization
 Slides 27 – 28
Matrix Powers
 Slides 29 – 30
Symmetric Matrices
 Slides 31 – 33
Orthogonal Matrices
 Slides 34 – 35
Hermitian Matrices
 Slides 36 – 38
Systems of First Order Differential Equations
 Slide 39
Systems of Second Order Differential Equations
 Slides 40 – 41
Stretched Membrane
Workbook 23 – Fourier Series
 Slides 1 – 4
Amplitude, period, frequency and angular
frequency
 Slides 5 – 7
Integrating Sine and Cosine
 Slides 8 – 13
Even and Odd functions
 Slides 14 – 15
Properties of even and odd functions
 Slide 16
Harmonic functions
 Slides 17 – 18
Will the functions contain a constant
 Slides 19 – 21
Calculate the Fourier series
 Slides 22 – 30
Find Fourier coefficients
 Slide 31
Fourier Sine series
Workbook 27 – Multiple Integration
 Slides 1 – 8
Theory questions
 Slides 9 – 11
Evaluate double integrals
 Slides 12 – 16
Which diagram represents the area of integration
 Slides 17 – 21
Reverse the order of integration
 Slides 22 – 26
Polar coordinates
 Slides 27 – 30
Evaluate integrals
 Slide 31
Express statement as an integral
 Slide 32
Centre of mass
 Slides 33 – 34
Evaluate the inner integral
 Slide 35
Moment on inertia
 Slides 36 – 37
Centre of pressure/gravity
Workbook 28 – Differential Vector Calculus
 Slides 1 – 2
Contours
 Slide 3
Closed Contours
 Slide 4
Unit Vectors
 Slides 5 – 7
Grad
 Slides 8 – 11
Divergence
 Slides 12 – 14
Curl
 Slides 15 – 16
Combining grad, div & curl
 Slide 17
Laplacian
 Slide 18
Rate of Change
 Slide 19
Vector Fields
 Slide 20
Differentiating Vectors
 Slide 21
Cylindrical Polar Coordinates
 Slides 22 – 23
Spherical Polar Coordinates
Workbook 29 – Integral Vector Calculus
 Pages 1 – 3
Finding Unit Normal
 Pages 4 – 5
Conservative Vector Fields
 Pages 6 – 15
Integrating Vectors
 Page 16
Current Continuity Equation
 Page 17
Double Integration of Vectors
 Page 18
Triple Integration of Vectors
 Page 19
Stokes’ Theorem
 Page 20
Gauss’ Law
 Page 21
Green’s Theorem