CCMAS Course Search

Elementary set theory, subsets, union, intersection, complements and Venn diagrams. Real numbers, integers, rational and irrational numbers. Mathematical induction, real sequences and series. Theory of quadratic equations and binomial theorem. Complex numbers, algebra of complex numbers and the Argand diagram. De-Moivre’s theorem and nth roots of unity. Circular measure, trigonometric functions of angles of any magnitude, addition and factor formulae.

Function of a real variable, graphs, limits and idea of continuity. The derivative, as limit of rate of change. Techniques of differentiation. Extreme curve sketching. Integration as an inverse of differentiation. Methods of integration and definite integrals. Application to areas and volumes.

Basic concept of Engineering Surveying. Feasibility study in engineering surveying. Primary line and control for mapping an area. Route Surveys. Definition, classification and uses of curves and curves formulae. Methods of setting out simple, compound, reverse, transition and vertical curves. Longitudinal and cross sectioning. Super-elevation. Setting out with theodolites, rectangular grid and polar coordinates. Establishment and construction of benchmarks and industrial setting out. Computation of area and volumes of earthwork using trapezoidal rule, Simpson and prismoidal rules, graphical and give and take methods. Cuttings and embankments, Eccentricity, Pappus theorem and Mass haul diagram.

Concept of entrepreneurship (Entrepreneurship, Intrapreneurship/Corporate Entrepreneurship,). Theories, Rationale and relevance of Entrepreneurship (Schumpeterian and other perspectives, Risk-Taking, Necessity and opportunity-based entrepreneurship and Creative destruction). Characteristics of Entrepreneurs (Opportunity seeker, Risk taker, Natural and Nurtured, Problem solver and change agent, Innovator and creative thinker). Entrepreneurial thinking (Critical thinking, Reflective thinking, and Creative thinking). Innovation (Concept of innovation, Dimensions of innovation, Change and innovation, Knowledge and innovation). Enterprise formation, partnership and networking (Basics of Business Plan, Forms of business ownership, Business registration and Forming alliances and joint ventures). Contemporary Entrepreneurship Issues (Knowledge, Skills and Technology, Intellectual property, Virtual office, Networking). Entrepreneurship in Nigeria (Biography of inspirational Entrepreneurs, Youth and women entrepreneurship, Entrepreneurship support institutions, Youth enterprise networks and Environmental and cultural barriers to entrepreneurship). Basic principles of e-commerce.

Nature of universe and solar, stellar and satellite systems. The motion of planets, Normal orbit, Kepler’s laws and perturbed orbit of satellite. The motion and the relationship of the earth and the sun/star. Stars constellations, magnitude and distance of sun/star from the earth. Solution of astronomical triangle. Celestial coordinate system. Time system, Star catalogues and charts. Uses of stars almanac. Solar and stellar observations. Processing of observations for the determination of azimuth.

Space and time. Units and dimension. Vectors and scalars. Differentiation of vectors. Displacement, velocity and acceleration. Kinematics, Newton laws of motion (Inertial frames, Impulse, force and action at a distance, momentum conservation). Relative motion. Application of Newtonian mechanics, equations of motion, conservation principles in physics, conservative forces, conservation of linear momentum, kinetic energy and work. Potential energy, system of particles and centre of mass. Rotational motion; Torque, vector product, moment, rotation of coordinate axes and angular momentum. Polar coordinates, conservation of angular momentum and circular motion. Moments of inertia, gyroscopes and precession. Gravitation: Newton’s law of gravitation, Kepler’s Laws of planetary motion, gravitational potential energy, escape velocity, satellites motion and orbits.

Heat, temperature and temperature scales. Gas laws; general gas equation, thermal conductivity. First Law of thermodynamics, heat, work and internal energy. Reversibility, second law of thermodynamics, heat engines and entropy. Zero’s law of thermodynamics, kinetic theory of gases, molecular collisions and mean free path. Elasticity, Hooke's law, Young's, shear and bulk moduli. Hydrostatics, pressure, buoyancy, Archimedes' principles. Bernoulli’s equation and incompressible fluid flow. Surface tension, adhesion, cohesion, viscosity, capillarity, drops and bubbles.

Quantitative measurements. Treatment of measurement, errors and graphical analysis. Experimental techniques for studies of meters, oscilloscope, mechanical systems, electrical and mechanical resonant systems, light, heat, viscosity and others covered in PHY 101. Emphasis should be placed on the basic physical techniques for observation, measurements, data collection, analysis and deduction.

Variations in celestial coordinate system. Timing with stop watch and chronometer, time conversion and variations. Determination of azimuth by hour angle of E-W stars near Elongation. Determination of hour angle of the sun. Computation by hour-angle methods of the sun and correction to astronomic azimuth. Other methods of determining astronomic azimuth. Determination of latitude by circum-meridian altitudes, programme for circum-meridian observations. Observations and computations for the independent determination of latitude and longitude. Selection of pair E-W stars. Simultaneous determination of latitude and longitude (ASTROFIX). Laplace equation and stations and geodetic uses of astronomic positions.

Basic concept of geodetic surveying. Design, specifications, observational procedure, accuracy attainable for geodetic surveying. Control surveys using triangulation, trilateration and traversing, geodetic leveling. Determination of normal, dynamic and orthometric heights. Satellite station, Laplace station and equations for the control of geodetic surveys. Sources of errors and application of appropriate corrections. Computations of geodetic coordinates. Adjustment of geodetic survey networks. Production of geodetic reports and plans. Deformation surveys and monitoring of large structure.