Name of the Programme BEng (GCU) Name of Module with Code Technical Mathematics 2 (M2G121464) Name of the Module Leader/Tutor Mr. K. Amarender Reddy Name of the course work Assignment Assessment weightage 24% Date of submission 09th May, 2016 Aim To build on the work of Level 1 and extend those aspects of Mathematics required in this and later stages of the degree Programme. Objective To make sure that students achieve the following learning outcomes. - to emphasize on mathematical notations, concepts and problem solving. - to develop competence in relevant applied mathematics concepts and application to engineering problems A. Knowledge and understanding of the topic This is the factual foundation of the assignment. The essential facts should be accurate and broad enough in their scope to allow further application. It includes to  Apply the knowledge of the Fourier series, half range sine and cosine series.  Evaluate double integrals in Cartesian coordinates and by change of order of integration.  Evaluate triple integrals in Cartesian coordinates and apply the knowledge.  Understand analytic functions, mappings, Taylor and Laurent series, singularities. B. Application and analysis of the topic (Module specific Skill) This is the way in which you analyze/ examine the factual information and how you interpret this information to add value to your answer (this could be in the form of conclusions, solutions, recommendations, etc.). It is also important to remember that the assessor must logically be able to follow the information in assignment submissions. It is expected whether the student has  Fundamentals of the module  Analytical skills of the module  Numerical Skills of the module  Acquired Knowledge to transform it to Engineering Applications Central Quality Office Rev:20th Jan 2016 F/QAP/021/001 C. The structure in terms of logic and coherence Submissions should have a clear start and a clear end. Information within submissions should also be logical and well grouped. Report structure, Abstract, Introduction & Referencing, Result Analysis, and Conclusion & Future works. D. The use of relevant work examples and/or examples gained from further reading Suggestions for further reading are contained within the course work and indicated at the end of the course work. These reading lists are not exhaustive and candidates are encouraged to read further and reference at the end of the course work using Harvard style of referencing. Marking scheme Component Weightage Total Marks Knowledge and understanding of the topic 30% 24 Application and analysis of the topic (Module specific Skill) 35% 28 The structure in terms of logic and coherence 30% 24 The use of relevant work examples and/or examples gained from further reading 5% 4 Please note all assignments shall subject to plagiarism. Plagiarism It is important to understand what plagiarism is and how it can be avoided. "Unacknowledged copying from published sources (including the internet) or incomplete referencing". The following also constitute plagiarism: • Copying sections of work from a friend/colleague. • Having a friend/family member dictate something to you. • Copying and pasting from the internet without citing the source. • Copying directly from a study text quotation without citing the source. Quotations When using quotations from books, websites or journal articles you should cite the author and the year of publication then use the quote in quotation marks. Paraphrasing Paraphrasing is where you encapsulate another person's original idea, argument or conclusion in your own words. It is still necessary to attribute those ideas to the author, and you can do this by using the formatting outlined above for direct quotations, taking care to include the author's surname and the year of publication. Central Quality Office Rev:20th Jan 2016 F/QAP/021/001 Collaboration We acknowledge that you may undertake joint study with colleagues or as part of a formal training Programme. However, working with another person to write assignments is not acceptable. Your answers must be your own and in your own words. Referencing Harvard Referencing (CCE Style) First Edition 2013 should be followed for both in-text and listing references. This downloadable document can be found in our CCE portal at:http://portal.cce.edu.om/member/contentdetails.aspx?cid=628 Ebrary Referencing Extended ebrary referencing is required to answer some of the questions as mentioned Instructions 1. Plagiarism is a serious offence. In case of any plagiarism detected, penalty will be imposed leading to zero mark. 2. Course work and reports should be solved by the individual/group. 3. Course work and reports should be submitted on time and submission after deadline will be marked zero. 4. Course work should be submitted with an appropriate cover page, which can be obtained from the departmental assistant at the department. 5. Name, student identification and title of the course work to be written clearly and legibly on the cover page. 6. The completed course work is to be submitted to the departmental assistant on or before the deadline and record your name, date of submission and signature in the book with the departmental assistant. Grading of Course work  Outstanding 90% and above  Excellent contribution 80% -89%  Very Good Contribution 70% - 79%  Good Contribution 60% - 69%  Satisfactory Contribution 50% - 59%  Inadequate Contribution Less than 50% Name and Signature of Module leader Mr. K. Amarender Reddy Date: CALEDONIAN COLLEGE OF ENGINEERING, OMAN DEPARTMENT OF MATHEMATICS & STATISTICS M2G121464: TECHNICAL MATHEMATICS 2 Assignment –Sem B-February 2016 Technical Mathematics 2 (M2G121464) Assignment Page 1 of 2 1. The final signal recovery using the process of modulation, demodulation and frequency domain filtering was found to be periodic with period and is defined by ( ) { Find the Fourier series expansion for ( ) [10] 2. Evaluate ∫∫ √ over the region bounded by the semi-circle lying in the first quadrant [10] 3. Find the volume bounded by the elliptic paraboloids and [10] 4. Prove that the Fourier series expansion of the function can be expressed as ∑ . [10] 5. Evaluate the double integral by changing the order of integration in ∫∫ ( ) over the positive quadrant of [10] 6. In a two dimensional fluid flow, the stream lines is given by ( ) Find the corresponding stream function and its complex potential. Also verify whether stream lines and the stream function are harmonic. [10] CALEDONIAN COLLEGE OF ENGINEERING, OMAN DEPARTMENT OF MATHEMATICS & STATISTICS M2G121464: TECHNICAL MATHEMATICS 2 Assignment –Sem B-February 2016 Technical Mathematics 2 (M2G121464) Assignment Page 2 of 2 7. Determine the analytic function ( ) ( ) and ( ) [10] 8. Find the Laurent's series expansion of ( )( ) for a) | | b) | | √ c) | | [10] For detailed study of pedagogical things concerning this part of coursework, refer to the following Ebrary resources. 1. Fourier Analysis and Boundary Value Problems, Gonzalez- Velasco, A. Enrique http://site.ebrary.com/lib/caledonian/detail.action?docID=10190334&p00=fourier+series 2. A Textbook of Engineering Mathematics, Pandey , Rajesh, Volume -1 and 2 http://site.ebrary.com/lib/caledonian/detail.action?docID=10416597&p00=complex+varia bles,http://site.ebrary.com/lib/caledonian/detail.action?docID=10416580&p00=complex+ variables **********