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Preface 5 Acknowledgements 6 Contents 7 1 Trigonometry 10 Philip Prewett 10 1.1 Trigonometric Relationships 11 1.2 Pythagoras' Theorem 12 1.3 The Sine and Cosine Rules 13 1.3.1 Sine Rule 13 1.3.2 Cosine Rule 14 1.4 Compound Angles 14 1.5 Derivatives of the Circular Functions 15 2 Real and Complex Numbers 17 Philip Prewett 17 2.1 Surds 18 2.2 Solution of Quadratic Equations 19 2.2.1 Equations Which Can Be Factorized 19 2.2.2 Equations Which Cannot Be Factorized 19 2.3 Complex Numbers 20 2.4 Euler's Theorem 23 2.4.1 De Moivre's Theorem 23 2.5 Phase Ambiguity 24 3 Vector Algebra 25 Philip Prewett 25 3.1 Addition of Vectors 26 3.2 Subtraction of Vectors 28 3.3 Multiplication of Vectors 29 3.3.1 Mutually perp Vectors 30 3.4 Direction Cosines 31 3.5 Position Vector r 32 3.6 Vector/Cross Product 33 3.6.1 Cartesian Form of Vector Product 33 3.7 Applications of Vectors 34 3.7.1 Work Done by a Force on a Body 34 3.7.2 Moment of Force (Torque) 35 4 Matrices 36 Philip Prewett 36 4.1 Basic Matrices 37 4.1.1 Addition and Subtraction of Matrices 37 4.1.2 Multiplying a Matrix by a Scalar 38 4.1.3 Multiplication of Matrices 38 4.1.4 Square Matrices 38 4.1.5 Transpose of a Matrix AT 39 4.2 Origins o

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