DEPARTMENT OF MATHEMATICS

This study develops and applies stochastic process models to design an optimized solar-powered battery swapping hub for electric tricycles (Kekes) in Benin City, Nigeria, with the aim of reducing urban CO2 emissions. Using first-order Markov chains to model solar irradiance variability and non-homogeneous Poisson processes to capture time-varying vehicle arrival patterns, the research addresses the inherent uncertainty in both energy supply and demand. Queueing theory analysis estimates service quality metrics, while Monte Carlo simulation-based optimization determines optimal battery inventory levels balancing capital investment against system reliability. Theproposedsystemcomprises228solarpanels(91.2kWcapacity)and60lithiumiron phosphate batteries (180 kWh total storage), designed to serve approximately 95 Kekes daily during 12-hour operations (6 AM to 6 PM). Comprehensive simulations validate system performance across 100 annual cycles, projecting 96.1% service reliability and 94.4% solar energy independence. The system achieves annual CO2 emission reductions of approximately252metrictonsthroughdisplacementoffossilfuelcombustion,representing a 97% per-vehicle reduction. Economic analysis indicates a 4.3-year payback period with 22.7% internal rate of return and net present value of N11.66 million over 20 years. A small-scale prototype operated continuously for 30 days validates the theoretical framework through empirical data collection, demonstrating close agreement between predicted and observed performance across all metrics (within 3% error). Sensitivity analyses confirm system robustness under parameter variations of ±20% in arrival rates and ±10% in solar irradiance, with solar resource availability identified as the dominant performance driver. 5 The methodology presented provides a replicable framework for designing renewable energy-powered transportation infrastructure under uncertainty, applicable to similar urban contexts across developing nations. The integration of multiple stochastic processes, validatedthroughbothsimulationandempiricaltesting,demonstratesthatmathematically rigorous approaches can effectively guide sustainable infrastructure investment decisions

Rice remains one of Nigeria’s most important staple crops, serving as both a major source of food and a significant contributor to national agricultural output. However, inconsistencies in production statistics and yield estimates have made it difficult to accurately assess the country’s progress toward self-sufficiency. This study, therefore, focuses on developing a rigorous mathematical framework for estimating and analyzing rice yield in Nigeria from 1990 to 2022. The research integrates statistical modeling and mathematical reasoning to provide a more objective and quantifiable understanding of yield dynamics, while addressing uncertainties associated with data collection, reporting errors, and environmental variability. The study utilizes secondary data from the Food and Agriculture Organization’s FAOSTAT database, which provides national figures on rice production and harvested area. The mathematical model adopts the classical yield equation � = �/� where � denotes yield (t/ha), � represents production (tonnes), and � is harvested area (hectares). To estimate the reliability of calculated yields, the propagation of uncertainty formula �� = � �� � 2 + 𝛿 � 2 was applied, allowing error terms in production and area to be combined mathematically. Statistical regression models (linear, exponential, and polynomial) were used to evaluate long-term yield trends and to test the hypothesis of yield improvement over time. In addition, stochastic simulation techniques and correlation analyses were introduced to capture the variability and interdependence between production and land-use parameters. Findings indicate that Nigeria’s rice yield followed a fluctuating but generally upward trend, rising from an average of 1.5 �/ℎ� in the early 1990s to about 2.8 �/ℎ� by 2022. The regression analysis revealed a statistically significant positive trend, confirming gradual improvements in productivity over the years. However, the propagated error analysis showed that yield uncertainties ranged between 5 –10% depending on data completeness and measurement precision. This highlights persistent limitations in the reliability of agricultural data collection systems. The study concludes that mathematical modeling provides a robust foundation for understanding agricultural yield trends and recommends the integration of error analysis and predictive modeling into national data reporting frameworks. By combining quantitative rigor with empirical agricultural data, the research establishes a replicable approach for improving the precision of yield estimation in Nigeria and other developing economies.

Spectral methods have emerged as a powerful and highly accurate class of numerical techniques for solving partial differential equations (PDEs). Unlike traditional finite difference and finite element methods, spectral methods approximate solutions using global basis functions, such as Fourier series, Chebyshev polynomials, and Legendre polynomials, enabling exponential convergence for smooth problems. This work explores the mathematical foundation, implementation, and applications of spectral methods for solving PDEs. We discuss Fourier spectral methods for periodic problems and Chebyshev spectral methods for non-periodic domains, highlighting their spectral accuracy and efficiency. Furthermore, we analyze the advantages of spectral collocation and Galerkin methods in handling various boundary conditions and problem domains. Practical implementations are demonstrated through examples, including the heat equation, Poisson equation, and wave equation, showcasing the effectiveness of spectral discretization. Finally, we review recent advancements, including hybrid spectral methods, spectral element methods, and applications in scientific computing. The results illustrate the superiority of spectral methods in terms of accuracy and computational efficiency, making them a vital tool in modern numerical analysis for solving PDEs.

Linear programming is one of the most effective techniques used in decision-making and optimization problems, especially in business and industrial applications. This project focuses on the use of a linear programming to determine the most efficient way of maximizing profit and minimizing cost. Mouka Foam Company, Benin City, was used as a case study to demonstrate how mathematical models can support better production and resource allocation decisions The simplex method was applied to the formulated linear programming problem derived from the assumed but realistic data of Mouka Foam Company. The process involved defining the objective function, identifying the constraints, introducing slack variables, and systematically applying the simplex algorithm to reach an optimal solution. The entire computation was manually solved and verified to ensure the accuracy of results The result of the analysis shows that the simplex method provided an optimal solution that maximizes profit while minimizing production cost under the given constraints. The findings prove that linear programming is a reliable and efficient mathematical tool for managerial decision-making, especially in production planning and cost optimization.

This project work provides an overview on the application of linear algebra to artificial intelligence including natural language processing and machine learning. We discuss how linear algebra operations such as matrices, linear transformations, eigen values and eigen vectors, are used to optimize AI models, analyze complex data structures and enable efficient computation. Beginning with an overview of fundamental concepts in linear algebra, such as vectors, matrices, and linear transformations, the study delves into specific applications of these concepts in AI. One key area of focus is machine learning, where linear algebra forms the backbone of algorithms for tasks such as regression analysis, and principal component analysis for dimensionality reduction. This work also showcases the versatility of linear algebra by delving deep into the various reaches of linear algebra into many other fields and areas of study such as economics, physics and engineering.

Inventory control plays a critical role in optimizing operations, reducing costs, and ensuring efficiency in the manufacturing industry. This study explores the application of inventory control strategies in the manufacturing sector, using Guinness as a case study. It examines how effective inventory management techniques—such as Economic Order Quantity (EOQ), Just-in-Time (JIT), and Material Requirements Planning (MRP)—impact production efficiency, cost reduction, and overall supply chain performance. The research highlights the challenges Guinness faces in inventory control, including demand variability, stockouts, and holding costs, while also identifying solutions such as automation, real-time tracking, and data-driven forecasting. Findings suggest that implementing advanced inventory control mechanisms leads to improved operational efficiency, minimized waste, and enhanced profitability. This study provides valuable insights for manufacturers seeking to optimize inventory practices and maintain a competitive edge in the industry.

The Dynamics of infectious diseases are vital in the disease control in populations. The mathematical methods that describe these diseases models often are insoluble hence, the need for numerical approximations. Stage two Runge-Kutta methods are used to integrate the system of differential equations that evolves in the model formulation of the infectious diseases being studied.
The stability analysis of Runge-Kutta method is done using boundary bars plot. The solution and plots are carried out using MATHEMATICA program.

Second-order partial differential equations (PDEs) are fundamental in mathematical physics, engineering, and applied sciences. These equations involve second-order derivatives of an unknown function with respect to multiple independent variables. They are broadly classified into three types: elliptic, parabolic, and hyperbolic, based on their characteristic behaviour. Notable examples include the Laplace equation, the heat equation, and the wave equation, each governing essential physical phenomena such as steady-state distributions, diffusion processes, and wave propagation, respectively. Solutions to second-order PDEs often require analytical or numerical techniques, including separation of variables, Green’s functions, Fourier and Laplace transforms, and finite difference methods. Boundary and initial conditions play a crucial role in determining well-posed solutions. Recent advancements in computational methods, such as finite element analysis and deep learning-based PDE solvers, have significantly improved the ability to model complex systems.

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.

This project investigates improving pathfinding algorithms in Geographic Information Systems (GIS) by optimizing the calculation of geodesics. Geodesics refer to the shortest paths along the curved surface of the Earth, as opposed to straight lines drawn on a flat map. This is crucial for accurate navigation, especially over long distances. Traditional GIS pathfinding algorithms often rely on simpler Euclidean distance calculations, which can lead to significant errors.The objective of this study is to develop or improve upon existing methods for finding optimal geodesics paths within a GIS environment. This will enable more accurate and efficient navigation for various applications, such as: route planning for vehicles, pedestrians, and drones, search and rescue operations, ecological studies analyzing animal movement patterns. The study will explore different algorithms for calculating geodesics on a geoid (Earth's mathematical representation). This could involve techniques like Dijkstra's algorithm adapted for curved surfaces or A* search with appropriate heuristics for geodesic distances. The study might explore methods to optimize the pathfinding process. This could involve strategies like pre-computing geodesics for frequently used routes or implementing techniques to reduce computational complexity. This study by optimizing geodesics paths for navigation has the potential to significantly enhance the capabilities of GIS for various applications requiring accurate and efficientpathfinding.