Partial differential equations (PDEs) are powerful mathematical tools used to describe various physical phenomena in fields such as physics, engineering, and economics. In this study, numerical solution of PDEs was employed, focusing on one-dimensional heat and wave equations, using MATLAB. By employing finite difference methods, we discretize the PDEs and utilize MATLAB's computational capabilities to obtain numerical solutions. Surface plots are generated to visualize the behavior of the solutions over time and space. The article provides a comprehensive overview of the numerical techniques employed for solving PDEs in MATLAB, offering insights into the underlying mathematical principles and computational implementation. The significance of numerical solutions in understanding the behavior of physical systems and their applications in real-life scenarios was discussed. Specifically, we highlight the importance of PDEs in modeling heat transfer processes, such as diffusion and conduction, and wave propagation phenomena, including vibrations and oscillations. Furthermore, practical applications of PDEs in various fields, including engineering design, environmental science, and medical imaging are presented. The numerical solutions obtained using MATLAB enable researchers and practitioners to analyze complex systems, predict their behavior, and optimize design parameters. Additionally, the study contributes to the advancement of computational methods for solving PDEs, enhancing our ability to model and simulate diverse phenomena accurately. The study underscores the significance of numerical techniques in solving PDEs and their role in addressing real-world challenges. By leveraging MATLAB's computational capabilities, researchers can efficiently obtain solutions to complex PDEs, facilitating advancements in science, engineering, and technology.

Studies on the relationship between students’ previous results, and graduations are usually based on only the undergraduate sessional results. This study conducts a statistical analysis of student graduation patterns, specifically focusing on the relationship between students' academic performance at the time of admission – measured by their West African Examination Council, WAEC –their first-year results, and their overall performance upon graduation. The study explores the use of coding transformation of WAEC grades to a 5-point scale Grade Point Average/Cumulative Grade Point Average, GPA/CGPA. The goal is to determine whether a student's potential at the time of admission and his/her first-year CGPA could predict academic success at graduation. The study followed a well-defined data collection method and employed data analysis techniques including multiple linear regression, analysis of variance, and coefficient of determination. The results of the statistical analysis reveals that a student's performance in WAEC does not significantly affect university graduation outcome; indicating that a student's ability to graduate with an excellent or a poor result is independent on their performance in the WAEC examination. However, the study did find that a student's first-year academic results significantly contributed to his/her university graduation outcome. As a result, the study offered various recommendations on how students can achieve higher graduating grades.

Soil the bed rock for natural provision of macro and micro nutrients for plant growth and development. A soil is considered unhealthy when it can longer supply required nutrients for plant growth due to over use or degradation. To mitigate soil low fertility, agroforestry method of raising trees and crops together makes nutrients available continuously for crop production, through dropping of its parts as litter which decays to add organic matter and nutrients to soil. Soils sampled with soil auger from seven agroforestry trees farm lands namely Gmelina arborea Roxb., Treculia africana Decne., Tectona grandis Linn. f., Pentaclethera macrophylla Benth., Irvingia gabonensis (Aubry-Lecomte ex O’Rorke) Baill., Mangifera indica Linn., Annona muricata Linn. and Fallow farmland as control were evaluated for macro and micro elements using standard laboratory methods and results presented with the highest and smallest values from each parameters evaluated: pH: 5.6, 4.5(Fa and Pm);%N,OC:0.21,0.10(Pm, Fl and Ma),3.40,1.30(Pm and Ig);EC (µS/cm):151.0,88.0(Fl and Tg), P, Mn, Fe, Cu, Zn (mg/Kg): 72.10, 19 .60 (Ta and Ma),111.02, 46.27 (Ta and Tg), 138.47,21.51(Pm and Am),1.53,0.80(Pm and Am), 8.08, 1.86(Ta and Mi); %Sand, Silt, Clay:88,70(Am, Ma and Tg), 16.50, 4.60(Ma and Tg, Am), 13.50,7.50 (Tg and Tg, Pm and Am); Ca, Mg, K, Na, Acidity, Al, ECEC(cmol/Kg)3.43, 0.59 (Ta and Tg),1.00, 0.24(Am and Mi), 0.15,0.07 (Pm, Ma, Ig and Am), 0.40,0.35(Tg, Ma, Ig and Am), 16.90,4.05(Tg and Am), 2.8,1.10(Tg and Am), 21.10,8.70(Tg and Am). We conclude by recommending agroforestry practice as way out of managing and sustaining soil health within the agroecosystems for continuous plant and food crop production as well sustaining the environment.