Calculus and Geometry

Instruction is in the form of lectures and exercises. Main course components: - Integrals: primitive functions, fundamental theorem of calculus, integration by substitution, partial integration, integration of rational functions, generalised integrals. - Applications of integrals: areas of plane domains, arc lengths, volumes of solids of revolution. - Ordinary differential equations: first order linear and separable differential equations, linear differential equations with constant coefficients, and integral equations. - Series: the concepts convergence and divergence, geometric series, comparison test, ratio test, integral test. - Vectors in the plane and space, scalar and vector product, lines and planes, distance between points, lines and planes. - Equations for surfaces and equations and parametric representations of curves.