UFH Mathematics
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Item A Practical Approach to Differential Calculus: MAT 122, Degree Examinations October/November 2024(University of Fort Hare, 2024-10) Funani, S.; Prins, A.L.Item A Practical Approach to Differential Calculus: MAT 122, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Funani, S.; Prins, A.L.Item A Practical Approach to Integral Calculus: MAT 123, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Mahlasela, Z.; Ndiweni, O.Item A Theoretical Approach to Differential Calculus: MAT 121, Degree Examinations October/November 2024(University of Fort Hare, 2024-11) Maqekeni, S.; Ndiweni, O.Item A Theoretical Approach to Differential Calculus: MAT 121, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Maqekeni, S.; Ndiweni, O.Item Abstract Algebra: MAT 311, Degree Examinations June 2017(University of Fort Hare, 2017-06) Makamba, B.B.; Murali, V.Item Abstract Algebra: MAT 311, Degree Examinations June 2023(University of Fort Hare, 2023-06) Makamba, B.B.; Nkonkobe, S.Item Abstract Algebra: MAT 311, Degree Examinations May/June 2025(University of Fort Hare, 2025-05) Prins, A.L.; Seretlo, T.T.Item Abstract Algebra: MAT 311, Degree Examinations November 2018(University of Fort Hare, 2018-11) Makamba, B.B.; Murali, V.Item Advanced Applied Mechanics: MAQ 521, Degree Examinations November 2018(University of Fort Hare, 2018-11) Mahlasela, Z.; Lubczonok, G.Item Advanced Mathematics Methods: MAP 511, Honours Examinations June 2023(University of Fort Hare, 2023-06) Mahlasela, Z.; Dukuza, K.Item Advanced Numerical Differentiation and Integration: MAP 312, Degree Examinations June 2023(University of Fort Hare, 2023-06) Childs, S.J.; Dukuza, K.Item Advanced Numerical Differentiation and Integration: MAQ 522, Degree Examinations November 2018(University of Fort Hare, 2018-11) Childs, S.J.; Lubczonok, G.Item Complex Analysis: MAT 322, Degree Examinations October/November 2024(University of Fort Hare, 2024-10) Prins, A.L.; Nkonkobe, S.Item Complex Analysis: MAT 322, Supplementary Examinations January 2019(University of Fort Hare, 2019-01) Ndiweni, O.; Murali, V.Item Complex Analysis: MAT 322, Supplementary Examinations November 2024(University of Fort Hare, 2024-11) Prins, A.L.; Nkonkobe, S.This supplementary examination paper for MAT 322, "Complex Analysis," is a 3-hour assessment worth a maximum of 100 marks. Students are required to answer five questions. The paper covers various advanced topics in complex analysis. The first section of the exam consists of multiple-choice questions testing foundational concepts such as the image of a line under a linear transformation, limits of complex functions, differentiability of complex functions, convergence of sequences, and regions of convergence for complex series. It also includes finding values of complex numbers for which an exponential equation holds. The second section focuses on properties of complex functions, requiring students to prove whether a given function is entire, define elementary functions like the complex cosine function and prove its differentiability and derivative, and demonstrate that a specific function is harmonic, subsequently finding its harmonic conjugate. A portion of the exam delves into contour integration and Cauchy's theorems. Students are required to evaluate contour integrals using the Cauchy Integral Formula and the Cauchy-Goursat theorem, and apply the Cauchy Integral Formula for derivatives to compute specific integrals. Further sections cover Taylor and Laurent series expansions and singularity classification. This includes computing the Taylor series for a given function centered at a specific point and finding its interval of convergence. Students must also compute the Laurent series representation for a function in a given domain and classify the singularities of another function. The examination also includes a section on residue theory, requiring students to state the Cauchy Residue Theorem, find residues of functions at given poles, and use the theorem to evaluate contour integrals.Item Computational Methods: MNU 122, Supplementary Examinations January 2019(University of Fort Hare, 2019-01) Nxala, B.E.; Mahlasela, Z.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 Functional Analysis: MAT 507, Supplementary Examinations January 2019(University of Fort Hare, 2019-01) Ngcibi, S.; Murali, V.Item Fundamentals, MAT 212, Degree Examinations June 2023(University of Fort Hare, 2023-06) Appiah, I.K.; Ndiweni, O.
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