MA231 Vector Analysis Notes | Assignment Help | Syllabus
Country: United Kingdom
University: The University Of Warwick
The main objectives
This module aims to: 1. teach a practical ability to work with functions of two or three variables and vector fields; 2. present the Gauss and Stokes theorems as higher-dimensional generalizations of the fundamental theorem of calculus; 3. present the theorems of Gauss and Stokes as generalisations of the fundamental theorem of calculus; 4. present the theorems of Gauss and Stokes as generalisations of the fundamental theorem
3. As a result of the Cauchy-Riemann equations and the divergence theorems, prove Cauchy’s theorem in complex analysis. 4. Teach the Cauchy integral formula, Taylor expansions, and residue calculus, as well as the rudiments of complex analysis that result from Cauchy’s theorem.
The main learning outcomes
A student should be able to compute line, surface, and volume integrals in generic curvilinear coordinates after completing this subject. 2. Know and apply the basic findings of vector calculus, such as the divergence theorem and Stokes’ theorem, in a range of situations. 3. Recognize the relationship between the presence of a scalar or vector potential in a vector field and the vanishing of that vector field’s curl or divergence, and be able to compute the potential when it occurs. 4. Be able to establish the Cauchy-Riemann equations for a complex differentiable function and prove Cauchy’s theorem from the integral theorems of vector calculus; 5. Be able to prove Cauchy’s integral formula from Cauchy’s theorem and use the integral formula to establish differentiability and series properties of complex differentiable functions using the integral formula; 6. Know how to compute Taylor expansions and residues, as well as how to apply them in the assessment of definite integrals and series summation.
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