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CONTENT OUTLINE

MAT 202 CONTENT(3 UNIT)First order ordinary differential equations. Existence and uniqueness of solution. Second-order ordinary differential equations with constants. Coefficients. General theory of nth-order linear ordinary differential equations. The laplace transform method. Simple treatment of partial differential equations in two independent variables. Application of ordinary and partial differential equation to physical, life and social sciences.

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Detailed study of the morphology. Taxonomy. Paleoecology and stratigraphic distribution and evolutionary trends of the major invertebrate phyla. Theories of evolution and the fossil record extinction of organisms and its causes.

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Impulse and momentum, conservation of momentum; work, power and energy, work and energy principle, conservation of mechanical energy, direct and oblique impact of elastic bodies. General motion of a particle in two dimensions, motions in a horizontal and vertical cirble; simple harmonic motion; motion of a particle attached to a light inelastic spring or string. Motion of a rigid body about a fixed axis; moments of inertia calculations; perpendicular and parallel axis theorems; principal axes of inertial and directions. Conservation of energy. Compound pendulum. Conservation of angular momentum.

System of linear equations, change of basis, equivalence and similarity. Eigen values and eigenvectors. Minimum and characteristic polynomial of a linear transformation. Cayley-hamilton theorem, bilinear and quadratic forms, orthogeonal diagonalisation canonical forms.

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Solution and algebraic and transcendental equation. Curve fittings, error analysis, interpolation. Zeros of non-linear equations of one variable. Systems of linear equation numerical differentiation and integration. Numerical solution of initial value problems for ordinary differential equation.

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The Galilean transformations and electromagnetic theory. The Michelson-Morley experiment and interpretations. Einstein postulates Simultaneity. The Lorentz translform. Time dilation. The mtwin paradox. Relativistic kinematics and dynamics. Experimental verification. Stem Gerlach experiment and electron spin.

The spin-orbit interaction, total angular momentum. Relativistic corrections to oneelectron atom. The hydrogen atom and four principal quantum numbers. Many electron atoms-pauli exclusion principle; the periodic table alkali atom spectra. LS and JJ coupling schemics of angular momenta. The normalZeeman effect. The composition of nuclei. Nuclear sizes, nuclear masses and abundances. Nuclear models. Alpha-beta-gamma radioactivity and fusion. Nuclear energy. Nuclear forces. Acceleration. Effects of radiaton on matter. Electrical properties of materials. Semiconductors, insulators. Electrons in solids, properties of elementary particles and particles detectors.

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The law of thermodynamics. Thermodynamic temperatures, heat and internal energy, reversibility, entropy. Free energies, application of thermodynamics to simple system-chemical potential, phase equilibrium and the phase rule, electrical potential, magnetism, surface energy. Absolute zero and low temperature phenomena. Third law of thermodynamics. Mathematical formulation of thermodynamics exact differentials and state functions, transformation relations for systems of two independent variables. Maxwell’s relation and legendry transformations Kinetic theory of gases thermodynamics exact differentials and state functions. Transformation relations for systems of two independent variables. Maxwell’s relations and legenre transformations. Kinetic theory of gases.

Solar atmosphere solar radiation emitted by the sun. The earth’s atmospheres. Effects of the earth’s atmosphere on solar radiation reaching the earth. Atmospheric electricity. The lonosphere and radio communication

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The course is basically an introduction to geophysics prospecting which comprises the magnetic gravity seismic and radioactive methods. Instruments, theory and data interpretation are described for each method.

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IDEA OF QUANTUM STATES,L ORBITAL SHAPE AND ENERGY, MOLECULAR ORBITAL THEORY AND SIMPLE VALENCE THEORY, ELECTROREPULSION THEORY, ATOMIC SPECTRA. METHOD OF DETERMINING MOLECULAR SHAPE, BOND LENGTHS AND ANGLES. THE STRUCTURE AND CHEMISTRY OF SOME REPRESENTATIVE MAIN GROUP ELEMENT AND COMPOUNDS.

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(a) SOURCE OF CHEMICALS AND ENERGY. INVENTORY OF NIGERIA’S NATURAL RESOURCE, RESOURCE DEPLETION RENEWABLE AND NON-RENEWABLE RESOURCES RECYCLING. ENVIRONMENTAL EFFECTS OF THE CHEMICAL INDUSTRY.

(b) EXTRACTIONS OF SELECTED METALS FEATURING PROCESSING OF ORES, THERMAL AND ELECTROLYTIC REDUCTION METHODS. PURIFICATION PROCESSES. USES OF THESE METALS, CORROSION AND PASIVITY

Theory of errors; statistical treatment of data; theory of sampling chemical methods of analysis including volumetric, gravimetric and physiochemical methods. Optical methods.

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Crystals and their characteristics; crystallographic notations. Crystal structure and crystal lattice. The bravals lattices and the seven crystals systems. Elements of symmetry and the thirty-two crytal classes. Brief survey of morphological optical and x-ray techniques in crystallography. Minerals and mineral composition, concepts of solid solution, ex-solution, atomic substitutions, isomorphism and polymorphism in minerals. Physical and chemical properties of minerals. Brief survey of physical, chemical and x-ray methods employed in minerals identification. Laboratory exercises on the above topics.

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Detailed study of the morphology. Taxonomy. Paleoecology and stratigraphic distribution and evolutionary trends of the major invertebrate phyla. Theories of evolution and the fossil record extinction of organisms and its causes.

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Practical introduction to basic field mapping techniques, field equipment and correct recording of geological features and information. Campus and township mapping exercise.

Basics concepts in ecology. The ecosystem and community structure. The ecological factors affecting plant and animal in terrestrial and aquatic habitats. Major terrestrial biomes. Productivity, energy flow and nutrient cycling.

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Light, phase contrast, dark field and electron microscopy, auto radiography, fluorescence. Handling and drawing under the microscope, preparation of slides (permanent and temporary). Biological drawings, magnification, calibration techniques. Photometry, colorimetry, chromatography conductometry experimental designs

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Physical and chemical processes in animal and plant physiology. Osmosis, diffusion, active transport, lon uptake and transport in plant and animals. Nature, properties and kinetics of enzymes. Osmoregulation. Cytochromes, metal proteins, structure and function of chlorophyll an chloroplast photosysthensis. Light and dark reactions. Nature of simple sugars and their polymers. Tissue respiration. Temperature on physiological processes.

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Chronological listing of important events. Experimental discoveries and the enunciation of ideas in the history of biochemistry. Contributions of the following biochemists to the subject: Nueberg. Emil fisher, warbury, michaelis-Menten, krebs, c. cori and G Cori, Hills, Ochoa, Calvin and Benson Watson and Crick. Jacob and Niremberg, Sanger, Kornberg and others.

Structures; properties and biological significance of proteins, carbohydrate, lipids and nuclei acid. Primary, secondary, tertiary and quartenary structures of proteins, determination of structures and biochemical application of proteins. Nomenclatures of nucleosides. Effects of acid and alkali on hydrolysis of nucleic acids. Structures and functions of major cell components, prokaryotic versus eukayotic