Vectors: plane and space vectors, dot and cross product, vector equations of lines and planes. Elementary linear algebra: geometric interpretation of linear equations, Gaussian elimination, definition of a vector space, span and subspace, basis, dimension. Matrices: transpose, determinants, rank and its application to linear systems, matrix inversion by cofactors. Series: partial sums, comparison and ratio tests, Maclaurin and Taylor series. Complex numbers: definition and properties, complex roots of a quadratic equation, complex numbers as vectors, modulus and argument, products and quotients, De Moivres theorem, exponential form, hyperbolic functions, loci in the Argand diagram. Ordinary differential equations: definitions, direction fields, linear first order differential equations, separable differential equations, modeling with first order equations, exact equations, numerical approximations, homogeneous second order equations with constant coefficients, fundamental solutions, complex and repeated roots of the characteristic equation, reduction of order, method of undetermined coefficients.
