Vectors; forces; sum of forces at a point; direction cosines and direction angles; components and component vectors; scalar and vector products; moment of a force; force systems on rigid bodies; equivalent force systems; couples; line of action of the resultant; equilibrium of a rigid body; friction; centre of mass; centroid; volumes; definite integration; moment of inertia of areas.

Kinematics of a particle: continuous and erratic rectilinear motion; curvilinear motion in the following coordinate systems: Cartesian, normal-tangential, cylindrical; pulley systems and relative motion. Kinetics of a particle: equations of motion – Newton 2 in all three coordinate systems; principle of work and energy; energy conservation; power; principle of linear impulse and momentum; conservation of linear momentum; impact.

Plane kinetics of rigid bodies; rotation and translation; absolute motion; relative motion; instantaneous centre of zero velocity. Properties of rigid bodies; definite and multiple integrals; Cartesian, polar, cylindrical and spherical coordinate systems; moments of inertia. Plane kinetics of rigid bodies; Newton's laws; energy methods. Vibrations of rigid bodies.

The straight line and the plane; space curves, derivatives and integrals of vectors, curves, the unit tangent, arc length; surfaces, partial derivatives of vectors, the gradient vector, vector fields, vector differential operators; line integrals, gradient fields; surface integrals in the plane, Green's theorem, surface integrals in space, Stokes' theorem; volume integrals; Gauss' divergence theorem; centres of mass and moments of inertia.

Mathematical modelling: correct identification of problems and specification of assumptions; formulation of ordinary and partial differential equations; analytical solutions; interpretation of a solution in terms of the initial problem.

Introduction to Matlab; zeros of functions; solving of systems of linear equations; numerical differentiation and integration; interpolation and curve fitting; numerical methods for solving ordinary and partial differential equations.