Browsing by Author "Prins, A.L."
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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 Abstract Algebra: MAT 311, Degree Examinations May/June 2025(University of Fort Hare, 2025-05) Prins, A.L.; Seretlo, T.T.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 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 Real Analysis, MAT 224, Degree Examinations October/November 2024(University of Fort Hare, 2024-11) Prins, A.L.; Ndiweni, O.