Browsing by Author "Katywa, N."
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Item Computational Methods: MNU 122, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Mtakazi, S.; Katywa, N.This supplementary examination paper for MNU 122, "Computational Methods," is a 3-hour assessment worth 100 marks. Students are required to answer all questions, which cover various topics in linear algebra, numerical methods, and mathematical modeling. Question 1 (18 marks) focuses on linear equations and matrix properties. It requires solving a system of linear equations using the Gaussian Elimination Method and proving a property related to matrix multiplication and addition for given matrices. Question 2 (35 marks) delves into linearizing non-linear equations and applying the least squares method. It asks students to express various non-linear equations in linear form. Subsequently, it presents a practical problem involving torque and diameter, where students must determine the best values for constants in a power law relationship using the least squares method from given data. Another part of this question involves finding the best values for constants in a reciprocal relationship from a given set of data. Question 3 (35 marks) covers differential equations and their applications. It defines a differential equation and asks students to determine the truthfulness of statements regarding the homogeneity, exactness, and linearity of given differential equations, correcting false statements. It then presents a real-world scenario involving the growth of supermarkets using a computerized checkout system, described by an initial value problem. Students must find the number of supermarkets at any time t and compute the number of supermarkets at a specific time (t=10). The question concludes with solving various types of differential equations (homogeneous, non-homogeneous, and Cauchy-Euler equations). Question 4 (12 marks) focuses on Laplace transforms. It requires showing properties of Laplace transforms, specifically for scaling and exponential functions, and finding the Laplace transform of a trigonometric function. It also involves working with a piecewise function and finding its Laplace transform. The examination aims to comprehensively assess students' theoretical understanding and practical application of computational methods in solving mathematical and real-world problems.Item Introduction to Analytical Methods: MAP 221, Degree Examinations October/November 2024(University of Fort Hare, 2024-10) Katywa, N.; Mahlasela, Z.Item Introduction to Analytical Methods: MAP 221, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Katywa, N.; Mahlasela, Z.This supplementary examination paper for MAP 221, "Introduction to Analytical Methods," is a 3-hour assessment worth 100 marks. The paper requires students to answer all questions, covering various topics in analytical mathematics. Question 1 focuses on differential equations, requiring students to define a differential equation, evaluate statements about their properties (like homogeneity, exactness, and linearity), and solve an initial value problem describing a real-world scenario. It also includes solving different types of second-order differential equations. Question 2 is dedicated to Laplace transforms. Students are asked to prove fundamental properties related to Laplace transforms and to find the Laplace transform of specific functions, including those defined piecewise. Question 3 covers Fourier series and special functions. It requires students to analyze a given trigonometric function, including sketching its graph and finding its corresponding Fourier cosine series to evaluate a specific infinite series. Additionally, students must demonstrate properties of the Gamma function and evaluate certain integrals involving Gamma and Beta functions. The examination aims to comprehensively assess students' analytical skills and their ability to apply various mathematical methods.Item Introduction to Business Mathematics: AMB 111F, Degree Examinations June 2023(University of Fort Hare, 2023-06) Katywa, N.; Appiah, I.K.Item Introduction to Numerical Mathematics: MNU 111, Degree Examinations June 2023(University of Fort Hare, 2023-06) Katywa, N.; Appiah, I.K.