http://repository.fuoye.edu.ng:80/handle/123456789/203 2026-04-16T05:16:58Z http://repository.fuoye.edu.ng:80/handle/123456789/297 Title: ELEMENTARY MATHEMATICS III Authors: FUOYE Abstract: Geometric representation of vectors in 1-3 dimensions, components, direction cosines. Addition, Scalar, multiplication of vectors, linear independence. Scalar and vector products of two vectors. Differentiation and integration of vectors with respect to a scalar variable. Two-dimensional co- ordinate geometry. Straight lines, circles, parabola, ellipse, hyperbola. Tangents, normals. Elementary Mathematics IV. Impact of two smooth sphere, and of a sphere on a smooth sphere Description: Geometric representation of vectors in 1-3 dimensions, components, direction cosines. Addition, Scalar, multiplication of vectors, linear independence. Scalar and vector products of two vectors. Differentiation and integration of vectors with respect to a scalar variable. Two-dimensional co- ordinate geometry. Straight lines, circles, parabola, ellipse, hyperbola. Tangents, normals. Elementary Mathematics IV. Impact of two smooth sphere, and of a sphere on a smooth sphere 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/296 Title: VECTOR AND TENSOR ANALYSIS Authors: FUOYE Abstract: Vector algebra. Vector, dot and cross Products. Equating of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vector integrate, line surface and volume integrals Greens Stoke's and divergence theorems. Tensor products of vector spaces. Tensor algebra. Symmetry. Gartesian tensers Description: Vector algebra. Vector, dot and cross Products. Equating of curves and surfaces. Vector differentiation and applications. Gradient, divergence and curl. Vector integrate, line surface and volume integrals Greens Stoke's and divergence theorems. Tensor products of vector spaces. Tensor algebra. Symmetry. Gartesian tensers 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/295 Title: VECTOR ANALYSIS Authors: FUOYE Abstract: Elementary Vector Algebra, Vector and Tripplre vector Products (more application solution of vector equation, plain curves and space curves. Geometrical equation of lines and planes. Linear independence of vectors; components of vectors, direction cosines; position vector and scalar products; senent frenent formulae; differential definition of gradients, divergent and simple multiplication) Description: Elementary Vector Algebra, Vector and Tripplre vector Products (more application solution of vector equation, plain curves and space curves. Geometrical equation of lines and planes. Linear independence of vectors; components of vectors, direction cosines; position vector and scalar products; senent frenent formulae; differential definition of gradients, divergent and simple multiplication) 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/294 Title: THEORY OF PARTIAL DIFFERENTIAL EQUATIONS Authors: FUOYE Abstract: Theory and solutions of first-order and second order linear equations. Classification, characteristics, cononial forms, Cauchy problems. Elliptic equations; laplace’s and posson’s formulase, properties of harmonic functions. Hyperbolic equations; wave equations, retarded potential; transmission line equation, Riemann method. Parabolic equation. Diffusion equation, singularity function, boundary and initial – value problem. Description: Theory and solutions of first-order and second order linear equations. Classification, characteristics, cononial forms, Cauchy problems. Elliptic equations; laplace’s and posson’s formulase, properties of harmonic functions. Hyperbolic equations; wave equations, retarded potential; transmission line equation, Riemann method. Parabolic equation. Diffusion equation, singularity function, boundary and initial – value problem. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/293 Title: THEORY OF ORDINARY DIFFERENTIAL EQUATIONS Authors: FUOYE Abstract: Differential equations: existence and uniqueness theorems dependence of solution on initial data and parameters. Properties of solutions. Sturm comparison and Sonin-Polya theorems. Linear and non-linear systems. Floguet’s theory and stability theory. Integral equations: classification, volterra and fredlhom types Neumann series. Fredholm alternative for degenerate Hilbert – Schmidt kernels. Reduction of ordinary differential equations to integral equations. Sysmmetric kernels, eigen function expansion with application. Description: Differential equations: existence and uniqueness theorems dependence of solution on initial data and parameters. Properties of solutions. Sturm comparison and Sonin-Polya theorems. Linear and non-linear systems. Floguet’s theory and stability theory. Integral equations: classification, volterra and fredlhom types Neumann series. Fredholm alternative for degenerate Hilbert – Schmidt kernels. Reduction of ordinary differential equations to integral equations. Sysmmetric kernels, eigen function expansion with application. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/292 Title: SYSTEMS THEORY Authors: FUOYE Abstract: Lyapunov Theorems. Solution of Lyapunov stability equation ATP + PA = Q. Controllability and observability. Theorem on existence of solution of linear systems of differential operations with constant coefficients. Description: Lyapunov Theorems. Solution of Lyapunov stability equation ATP + PA = Q. Controllability and observability. Theorem on existence of solution of linear systems of differential operations with constant coefficients. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/291 Title: SETS, LOGIC AND ALGEBRA I Authors: FUOYE Abstract: Introduction to the language and concepts of modern Mathematics. Topics include; Basic set theory: mappings, relations, equivalence and other relations, Cartesian products. Binary logic, methods of proof. Binary operations. Algebraic structures, semigroups, rings, integral domains fields. Homeomophics. Number systems; properties of integers, rationals, real and complex numbers. Description: Introduction to the language and concepts of modern Mathematics. Topics include; Basic set theory: mappings, relations, equivalence and other relations, Cartesian products. Binary logic, methods of proof. Binary operations. Algebraic structures, semigroups, rings, integral domains fields. Homeomophics. Number systems; properties of integers, rationals, real and complex numbers. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/290 Title: REAL ANALYSIS II Authors: FUOYE Abstract: Riemann integral of functions R.....)R, continous monopositive functions. Functions of bounded variation. The Riemann Strieltjes integral. Pointvise and uniform convergence of sequences and series of functions R.... )R. Effects on limits (sums) when the functions are continuous differentiable or Riemann integrable power series. Description: Riemann integral of functions R.....)R, continous monopositive functions. Functions of bounded variation. The Riemann Strieltjes integral. Pointvise and uniform convergence of sequences and series of functions R.... )R. Effects on limits (sums) when the functions are continuous differentiable or Riemann integrable power series. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/289 Title: REAL ANALYSIS I Authors: FUOYE Abstract: Bounds of real numbers, convergence of sequence of numbers. Monotones sequences, the theorem of nested Intervals. Cauchy sequences, tests for convergence of series. Absolute and conditional convergence of series and rearrangements. Completeness of real and incompleteness of rational. Continuity/and differentiability of functions R) R. Rolles's and mean value theorems for differentiable functions Taylor series. Description: Bounds of real numbers, convergence of sequence of numbers. Monotones sequences, the theorem of nested Intervals. Cauchy sequences, tests for convergence of series. Absolute and conditional convergence of series and rearrangements. Completeness of real and incompleteness of rational. Continuity/and differentiability of functions R) R. Rolles's and mean value theorems for differentiable functions Taylor series. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/288 Title: QUANTUM MECHANICS Authors: FUOYE Abstract: Particle wave duality.Quantum postulates.Schroedinger equation of motion. Potential steps and wells in 1-dim Heisenlberg formulation. Classical limit of Quantum mechanic. Computer brackets. Linear harmonic oscillator. Angullar momentum. 3-dim square well potential. The hydrogcn atom collision in 3-dim. Approximation methods for stationery problems Description: Particle wave duality.Quantum postulates.Schroedinger equation of motion. Potential steps and wells in 1-dim Heisenlberg formulation. Classical limit of Quantum mechanic. Computer brackets. Linear harmonic oscillator. Angullar momentum. 3-dim square well potential. The hydrogcn atom collision in 3-dim. Approximation methods for stationery problems 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/287 Title: Ordinary Differential Equation Authors: FUOYE Abstract: Ordinary differential equations: linear dependence, Wronskian, reduction order, variation of parameters, series solution about ordinary and regular points. Special functions: Gamma, Beta, Bessel, Lengendre, Hyper geometric. Laplace transform and applications to initial value problem Description: Ordinary differential equations: linear dependence, Wronskian, reduction order, variation of parameters, series solution about ordinary and regular points. Special functions: Gamma, Beta, Bessel, Lengendre, Hyper geometric. Laplace transform and applications to initial value problem 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/286 Title: OPTIMIZATION THEORY Authors: FUOYE Abstract: Linear programming models. The simplex Method: formulation and theory. Quality integer programming; Transportation problem. Two-person zero-sum games. Nonlinear programming: quadratic programming Kuhn-tucker methods. Optimality criteria. Simple variable optimization. Multivariable techniques. Gradient methods Description: Linear programming models. The simplex Method: formulation and theory. Quality integer programming; Transportation problem. Two-person zero-sum games. Nonlinear programming: quadratic programming Kuhn-tucker methods. Optimality criteria. Simple variable optimization. Multivariable techniques. Gradient methods 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/285 Title: NUMERICAL ANALYSIS II Authors: FUOYE Abstract: Finite difference equation and operations; Discrete variable methods for solution of IUPS -ODES. Discrete and continuous Tan methods for solving lLIP -ODES, error analysis. Partial differential equation. Finite difference and finite elements methods. Stability convergence and error analyses. Description: Finite difference equation and operations; Discrete variable methods for solution of IUPS -ODES. Discrete and continuous Tan methods for solving lLIP -ODES, error analysis. Partial differential equation. Finite difference and finite elements methods. Stability convergence and error analyses. 2015-03-02T00:00:00Z http://repository.fuoye.edu.ng:80/handle/123456789/284 Title: NUMERICAL ANALYSIS I Authors: FUOYE Abstract: Polynomial and splines approximation. Orthogunal polynomials and chebysev approximations. Direct and interactive methods for the solution of systems of linear equations. Eigen value problem -power methods, inverse power methods. Pivoting strategies. Description: Polynomial and splines approximation. Orthogunal polynomials and chebysev approximations. Direct and interactive methods for the solution of systems of linear equations. 2015-03-02T00:00:00Z