MATHEMATICS
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The academic level of the tutorials range from basic to advanced (level 1) and are placed in approximate order of difficulty.
ALGEBRA
TUTORIAL 1 - BASIC ALGEBRA Explain the use of Symbols. Exolain the Conformity of Units in Equations. Manipulate equations and Expressions The Distributive Law Products of Two Binomials
TUTORIAL 2 - STRAIGHT LINE LAWS Gradients Intercepts Proportional Relationships Inversely Proportional Relationships
TUTORIAL 3 - SOLUTION OF EQUATIONS Definitions Substitution Method Elimination Method Matrix Method Cubic Equations Graphical Solutions
TUTORIAL 4 - AREAS AND VOLUMES Areas of Geometric Shapes. Volumes of Geometric Shapes Surface Areas of Geometric Shapes
TUTORIAL 5 - LOGARITHMS Definitions Base Powers and Indexes Power Laws Applications Logarithmic Graphs
TUTORIAL 6 - SIMPLIFICATION AND EXPANSION Explain the Summation Symbol Explain and Use Factorials Explain and Use the Binomial Expansion
TUTORIAL 7 - EXPONENTIAL AND HYPERBOLIC FUNCTIONS Logarithmic equations with logarithms. Define the Exponential Function Linearise functions with logarithms Define the Hyperbolic Function Compare Hyperbolic and Trigonometric functions
TUTORIAL 8 - MATHEMATICAL SERIES AND PROGRESSIONS The sigma notation The binomial coefficent and Pascal's Triangle. Convergence and divergence. Limiting values. The binomial expansion and theorem. Maclaurin's expansion
TRIGONOMETRY
TUTORIAL 1 - BASIC TRIGONOMETRY Angular Measurement The Right Angle Triangle Trig Ratios Sine, Cosine and Tangent Sinusoidal Functions Harmonic Motion Frerquency and Periodic Time Angular Velocity
TUTORIAL 2 - MORE TRIGONOMETRY Revise Basics Cartesian and Polar Coordinates Sine Rule Cosine Rule The Areas of Triangles
TUTORIAL 3 - PERIODIC FUNCTIONS Phase and Displacement Square Waves Phasor Diagrams Complex Numbers
TUTORIAL 4 - TRIGONOMETRIC IDENTITIES Compound Angles Double Angles Half Angles Products and Sums Changing Cos to Sin and Sin to Cos Hyperbolic Functions
VECTORS
COORDINATE SYSTEMS Cartesian and Polar Co-ordinates. Cylindrical and Spherical Coordinates. Conversion Between Coordinates
BASIC VECTOR THEORY Cartesian and Polar Co-ordinates. Vector addition and subtraction. Vector resolution. Unit Vector Three Dimensional vectors Spherical coordinates
ADVANCED VECTOR THEORY Vector Products Dot or Scalar Product Cross or Vector Product Triple Scalar Product Triple Vector Product
MOMENTS OF AREA CENTROIDS AND FIRST MOMENTS OF AREA SECOND MOMENTS OF AREA PARALLEL AXIS THEOREM
PARTIAL FRACTIONS Division of Polynomials Remainder Theorem First Degree Partial Fractions Second Degree Partial fractions
STATISTICS AND PROBABILITY
STATISTICS TUTORIAL 1 Grouped and Ungrouped Data Mean and Median Ogives, Histograms and Bar Charts Qaurtiles Normal Distribution Variance and Standard deviation
STATISTICS TUTORIAL 2 Curve Fitting Method of Least Squares Use of Excel to Find Functions
STATISTICS TUTORIAL 3 Probability Permutations Combinations Events Multiple Events Sample Space
STATISTICS TUTORIAL 4 Sample Space Accumulative Probability Binomial Distribution Normal Distribution Poisson Distribution
MATRICES
BASIC MATRIX THEORY Definitions Column Vectors Arrays Diagonal, Unit, Zero and Transpose Matrices Trace of a Matrix Adding Arrays Multiplying Arrays
MORE MATRIX THEORY Representing Simultaneous Equations Determinants Minors and Cofactors The Adjoint Matrix The Inverse Matrix Solving Simultaneous Equations
EIGEN VALUES AND VECTORS Definitions The Power method Use of the Identity matrix
CALCULUS
INTEGRATION TUTORIAL 1 Basic Numerical Integration Finding Areas Under Graphs Standard Forms Integration Between Limits Moments of Area and Inertia
INTEGRATION TUTORIAL 2 Integrate Polynomials Integrate Trigonometric Expressions Integrate Logarithmic Expressions Integrate Exponentials Integration by Substitution Inegration by Parts
INTEGRATION TUTORIAL 3 Numerical Methods of Integration Areas under graphs Mid-ordinate rule Trapezoidal rule Engineerng Applications. Simpson's Rule
DIFFERENTIATION TUTORIAL 1 Gradients of functions Differential Coefficients Standard Forms Higher Order Differentials Engineerng Applications.
DIFFERENTIATION TUTORIAL 2 Differentiate a Sum Differentiate a Product Differentiate a Quotient Turning Points
MAXIMUM AND MINIMUM THEORY Turning points of functions Graphical determination. Determination by successive differentiation. Engineering examples
COMPLEX NUMBERS Argand Diagrams Polar Co-ordinates Multiplication and Division of Complex Numbers Conjugate Numbers Phasors and Phasor Diagrams Complex Impedance
LAPLACE AND FOURIER TRANSFORMS Transforms of common time functions Transform Tables Inverse Transforms Fourier transforms of basic functions of s Changing functions into complex numbers
ADVANCED MOMENTS OF AREA ADVANCED SECOND MOMENTS PRODUCT SECOND MOMENT UNSYMMETRICAL SECTIONS PRINCIPAL AXES MAXIMUM AND MINIMUM SECOND MOMENTS POLAR SECOND MOMENTS