Preface‎;‎ 1‎.‎ Mathematics and engineers‎;‎ 2‎.‎ Mappings‎;‎ 3‎.‎ The nature of generalisation‎;‎ 4‎.‎ Symbolic conditions for linearity‎;‎ 5‎.‎ Graphical representation‎;‎ 6‎.‎ Vectors in a plane‎;‎ 7‎.‎ Bases‎;‎ 8‎.‎ Calculations in a vector space‎;‎ 9‎.‎ Change of axes‎;‎ 10‎.‎ Specification of a linear mapping‎;‎ 11‎.‎ Transformations‎;‎ 12‎.‎ Choice of basis‎;‎ 13‎.‎ Complex numbers‎;‎ 14‎.‎ Calculations with complex numbers‎;‎ 15‎.‎ Complex numbers and trigonometry‎;‎ 16‎.‎ Trigonometry and exponentials‎;‎ 17‎.‎ Complex numbers‎:‎ terminology‎;‎ 19‎.‎ The logic of complex numbers‎;‎ 20‎.‎ The algebra of transformations‎;‎ 21‎.‎ Subtraction of transformations‎'‎ 22‎.‎ Matrix notation‎;‎ 23‎.‎ An application of matrix multiplication‎;‎ 24‎.‎ An application of linearity‎;‎ 25‎.‎ procedure for finding invariant lines‎,‎ eigenvectors and eigenvalues‎;‎ 26‎.‎ Determinant and inverse‎;‎ 27‎.‎ Properties of determinants‎;‎ 28‎.‎ Matrices other than square‎;‎ partitions‎;‎ 29‎.‎ Subscript and summation notation‎;‎ 30‎.‎ Row and column vectors‎;‎ 31‎.‎ Affine and Euclidean geometry‎;‎ 32‎.‎ Scalar products‎;‎ 33‎.‎ Transp‎.‎‎.‎‎.‎