CALEDONIAN COLLEGE OF ENGINEERING, MODULE HANDBOOK. Department of Mathematics and Statistics SULTANATE OF OMAN. BEng Programme.

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1 Module Code M3G Advanced Mathematics CALEDONIAN COLLEGE OF ENGINEERING, SULTANATE OF OMAN Semester A MODULE HANDBOOK BEng Programme dy dx + Py = Q Module Team ye P dx = Qe P dx dx + C lim n n n = e Mr Syed Zahoor Ul Haque Mr Amarender Reddy Dr K R Karthikeyan Dr A Senguttuvan Dr Padmavathi N Dr Javed Ali Dr Ahmed Ibrahim Department of Mathematics and Statistics

2 1. Module Details Programme Name BEng (Hons) in EIE/EPE Module Code Module Title Credits Level and Semester M3G Advanced Mathematics 20 Level 3 Semester B Pre Requisite Knowledge M2G Technical Mathematics 2 2. Aims And Objectives The aim of the module is to impart student with the ability to apply mathematics through vector calculus, important transforms, numerical solutions, and probability and statistics as applied to engineering problems applications. Learning is emphasized on the development of students ability to apply mathematics and statistics as a tool with understanding to solve engineering problems. The objectives are: 1 To emphasize on mathematical notations, concepts and problem solving. 2 To develop competence in relevant applied mathematics concepts and application to engineering problems. 3. Syllabus Probability and Statistics: Mean and standard deviation, coefficient of correlation and equation of regression lines, normal curve, confidence interval, testing of significance. Discrete, continuous & mixed random variables, Probability density function, cumulative distribution function, mathematical expectation, moments, moment generating function, special distributions. Vector Calculus: Scalar & Vector fields, gradient, curl, divergence, change of variables, line integrals, surface integrals, volume integrals, Green s theorem in a plane, Gauss divergence theorem and Stoke s theorem. Fourier and Z Transforms: Fourier transforms & Z transforms: Definition, Properties, Transforms of elementary functions and derivatives, Convolution theorem, some useful Z-transforms and applications. Numerical Solution of equations: Bisection method, fixed point iteration method, Newton-Raphson s method, Solution of linear system by Gauss elimination method, Inverse of a matrix by Gauss-Jordan method; Gauss-Jacobi and Gauss-Seidel methods. Numerical solution of Ordinary and Partial Differential Equations: Solution of ordinary differential equations-euler s method, Runge-Kutta method of order 4. Finitedifference techniques to reduce PDEs to matrix problems, implicit/explicit time stepping. 4. Learning Outcomes On successful completion of this module the student will be able to: 1 Determine measures of central tendency, coefficient of correlation and regression lines. 2 Apply the knowledge of normal distribution in fixing the confidence limits and testing the significance. 3 Apply basic concepts of probability & analyze probability distributions. 4 Distinguish scalar & vector fields and compute gradient, curl, divergence. 5 Apply the knowledge of line integrals, surface integrals and volume integrals on vector fields. 6 Compute Fourier Transform and its applications. 7 Compute Z Transform and its applications(am1, AM5) 8 Solve transcendental equations by numerical techniques. P2 P a g e

3 9 Solve the system of linear equations by numerical techniques. 10 Apply gained knowledge of numerical methods to solve ordinary differential equations. 11 Apply gained knowledge of numerical methods to solve partial differential equations. 5. Learning and Teaching Strategy Combination of lectures and tutorials: The module will be delivered in approximately 15 weeks of time. There are 6 contact hours per week divided in four sessions. During the lecture sessions as given in the module descriptor are presented. Problem solving sessions will also be conducted. Tutorial work will be given to the students at the end of each topic which the students solve in the presence of the teacher. Take home exercises are also provided for practice. Module Expectations: In addition to the above expectations, students should get expertise in any of the multi-paradigm numerical computing environment and fourth generation programming languages like Math lab. Developing any system requires integrating mechanical, electrical, control and embedded software subsystems. It is expected that this module would enable the students to design and simulate all of these domains in a single environment. At the end of the course, students must be able to understand and manage complex systems interactions. Further, be able to detect design inefficiencies and errors during early development of systems using predict and optimization techniques. 6. Weekly teaching schedule (i) Full time Mode Week No. Date of commencement of week 1 16-sep sep sep Oct Topics to be covered Referencing* ebrary* Remarks Overview of the Probability and Statistics: Mean and standard deviation, correlation coefficient and equation of regression lines, normal curve, confidence interval. Probability and Statistics contd. Testing of significance. Discrete, continuous & mixed random variables, Probability density function, cumulative distribution function, mathematical expectation. Probability and Statistics contd. moments, moment generating function, special distributions. Vector Calculus: Scalar & Vector fields, gradient, curl, divergence, change of variables. Vector Calculus contd. line integrals, surface integrals, volume integrals, Green s theorem in a plane. R5 Ch. 1-2 R5 Ch3, Ch8 R5 Ch8 R1-Ch8 R2, R4, R5 R1 Ch8 R2, R4, R6 E1 E1 P3 P a g e

4 5 14- Oct e-learning Oct Vector Calculus contd. Gauss divergence theorem and Stoke s theorem. Fourier and Z transforms: Fourier transforms, Definition, Properties, Transforms of elementary functions and derivatives, Convolution theorem Oct Assessment Week R1 Ch8, R6 R1 Ch22 R2, R6 E1& Quiz I (formative assessment) Midterm Examination 8 4- Nov Nov Nov Nov Dec Dec Dec Fourier and Z transforms contd.: Convolution theorem Fourier and Z transforms contd. Z-transforms, Definition, Properties, Transforms of elementary functions and derivatives, Convolution theorem. Fourier and Z transforms contd. Some useful Z-transforms and applications. Computation of Fourier transforms using Mathlab. Numerical Solution of Equations : Bisection method, Fixed point iteration method, Newton- Raphson s method, Solution of linear system by Gauss elimination method Numerical Solution of Equations contd. Solution of linear system Gauss-Jacobi and Gauss-Seidel methods, inverse of a matrix by Gauss-Jordan method Numerical solution of Ordinary and Partial Differential Equations. Solution of ordinary differential equations-euler s method, Runge-Kutta method of order 4. Numerical solution of Ordinary and Partial Differential Equations contd. Finite-difference techniques to reduce PDEs to matrix problems, implicit/explicit time stepping Dec Assessment Week Dec Assessment Week R1 Ch22 R2, R6 R1 Ch. 23 & Ch12 R1 Ch23 R1 Ch28 R1 Ch28 R1 Ch32 R2 Ch33 E1& E1, & E1, & E1, & E4 E1, & E4 Coursework Submission Quiz II (formative assessment) Feedback of Coursework to Students End term Examination Final Examination P4 P a g e

5 (ii) Part time Mode Week No. Date of commencement of week 1 16-sep sep sep Topics to be covered Overview of the Probability and Statistics: Mean, correlation coefficient and equation of regression lines, normal curve, and confidence interval. Probability and Statistics contd. Testing of significance. Discrete, continuous & mixed random variables, Probability density function, cumulative distribution function, Probability and Statistics contd. Moments, moment generating function, special distributions. Vector Calculus: Scalar & Vector fields, gradient, divergence, change of variables. Topics to be given during directed study hours (30% to 40 %) (2 hrs/week) standard deviation Mathematical expectation. Computing curl line integrals Referencing* ebrary* Remarks R5 Ch 1-2 R5 Ch3, Ch8 R5 Ch8 R1-Ch8 R2, R4, R5 E1 E1 Answers of all additional questions will be posted in CCE Learn. Students can submit the answers/ worksheet of additional problems to the module tutors for correction during their directed study hours 4 7- Oct Vector Calculus contd. surface integrals, volume integrals, Green s theorem in a plane. R1 Ch8 R2, R4, R Oct e-learning Oct Vector Calculus contd. Gauss divergence theorem and Stoke s theorem. Fourier and Z transforms: Fourier transforms, Definition, Properties, Transforms of elementary functions and Convolution theorem R1 Ch8, R6 R1 Ch22 R2, R6 E1& Quiz I (formative assessment) P5 P a g e

6 derivatives, Convolution theorem Oct Assessment Week Midterm Examination 8 4- Nov Nov Fourier and Z transforms contd.: Convolution theorem Fourier and Z transforms contd. Z-transforms, Definition, Properties, Transforms of elementary functions and derivatives, Convolution theorem. R1 Ch22 R2, R6 E1& R1 Ch 23 & Ch12 E1, & Nov Nov Fourier and Z transforms contd. Some useful Z-transforms and applications. Computation of Fourier transforms using Mathlab. Numerical Solution of Equations : Bisection method, Newton- Raphson s method, Solution of linear system by Gauss elimination method Fixed point iteration method Solution of linear system R1 Ch23 R1 Ch28 E1, & E1, & E4 Coursework Submission 12 2-Dec Numerical Solution of Equations contd. Gauss- Jacobi and Gauss-Seidel methods, inverse of a matrix by Gauss-Jordan method Euler s method R1 Ch28 E1, & E4 Quiz II (formative assessment) 13 9-Dec Dec Numerical solution of Ordinary and Partial Differential Equations. Solution of ordinary differential equations-, Runge-Kutta method of order 4. Numerical solution of Ordinary and Partial Differential Equations R1 Ch32 R2 Ch33 Feedback of Coursework to Students P6 P a g e

7 contd. Finite-difference techniques to reduce PDEs to matrix problems, implicit/explicit time stepping Dec Assessment Week Dec Assessment Week End term examination Final Examination *Referencing/ebrary/LinksDetails Reference Book Title& Author Link Grewal, B. S., Higher Engineering - R1 Mathematics.42 (Text Book) nd Ed.NewDelhi:Khanna Publishers. Kreyszig, E., Advanced Engineering - R2 Mathematics.10 th Ed. John Willey R3 R4 R5 R6 E1 E4 James, G., Advanced Modern Engineering Mathematics: Addison Wesley DASS, H.K., Advanced Engineering Mathematics. S. Chand & Co. Ltd. Hogg R. V., McKean J., Craig, A. T., Introduction to Mathematical Statistics, Pearson. Veerarajan, T., Engineering Mathematics: Tata McGraw-Hill. Pandey& Rajesh, 2010.Text Book of Engineering Mathematics: Vol.II. Lucknow, IND:Global Media Yang&Xin-She., Applied Engineering Mathematics. Cambridge, GBR:Cambridge International Science Publishing Ganesh, A. &Balasubramanian, G., 2009.Engineering Mathematics-II. Delhi, IND: New Age International. R K Bera et.al, Mathematical Physics for Engineers. New Academic Science Publishing - - Available from: = &p00=multiple+integrals [Accessed:13 July 2014] = &ppg=81&p00=laurent%20series [Accessed:13 July 2014] Available from: = &p00=multiple%20integrals%20vector%20calcu lus[accessed:24 June 2014] Available from: = &ppg=182&p00=laplace [Accessed:13 July 2014] P7 P a g e

8 7. Assessment Strategy Assessment Method The module assessment will consist of a maximum of 3 components for this module and as specified in the table below. Assessment Methods Type of module and assessment Midterm Coursework Final Assessment CW+FE Theory only 20% Assignment 30% Final Exam 50% Timeline 7 th week 10 th week After 13 th week Assessment Loading Coursework component Assessment Loading Weightage Level 3 25 to 50% Topics covering until 9th week will be included for testing almost 60% of the learning outcomes through midterm examinations, assignment (8 questions with/without subdivisions) and quizzes. All these will be considered as the components of Coursework. This module is assessed by Continuous Assessments (Midterm Examination and Coursework) and Final Examination. Sl. No. Type of assessment 1 Midterm Examination Description Marks Weightage Unseen written examination of 1½ hours duration (50 marks) % 2 Coursework Written assignment (100 marks) % Total CA (Continuous Assessments) 50% Quizzes will be given as formative assessment (for feedback, not for CA calculation) Unseen written examination of 3 hours duration 3 Final Examination % (100 marks) Total 100% Minimum pass requirement : To score a minimum of 45% in Continuous Assessments, 45% in Final Examination and 50% overall. P8 P a g e

9 8. Indicative Marking Threshold for Course Work for B Eng (Hons) in EIE/EPE/ POM/ CAME/ TE/ COE/ MT Indicative Mark 90% and above Outstanding 80-89% (EXCELLENT) 70-79% (VERY GOOD) 60-69% (GOOD) 50-59% (Satisfactory) <50% (FAIL) Commentary on Marking Standards Outstanding Truly outstanding work to be recognized in all aspects- New invention, novel technology, new idea worth applying for patent, evidence of excellent communication skills, clearly communicated report, results critically analyzed, alternate solutions and appropriate suggestions put forward Exceptionally superior work in both content and presentation Indicates highest level of achievement + points below Excellent Exceptionally clear, well-structured and theoretically informed. Standard of English excellent, Exceptionally good powers of analysis and interpretation. Adequate References Solutions to problems All steps in a meticulously structured manner Use of relevant units and interpretations, Use of intelligent and innovative methods + points given below High Displaying a thorough understanding of the topic. Focusing clearly on the question Demonstrate extensive reading to support analysis Soundness of judgment Coherently reasoned statement with empirical evidence. Suggestions for improvement Solutions to problems All steps in a structured manner with relevant units of quantities. Answers to show accurate results ( may miss simple steps) Good interpretations of Solution (may be incomplete) Generally Good Solid piece of work which answers the question, A clear conclusion in a generally focused and well written manner, Use of citations, quotations and references. Evidence of wider reading and deep analysis Solutions to problems Contain necessary /important steps with relevant units. Accurate results, (may miss some steps which are not very critical to problem solving) Reasonable level of interpretation of results. Proper referencing Average Substantial room for improvement, (e.g. in terms of the standard of written English, the sharpness of focus on the question) Insufficient analysis of the results References included, but not adequate Solutions to problems Steps for solving problem based on theory and principles (may lack some steps towards the final answers) No substantial interpretation of the final result Poor Exhibits some potential / degree of standard (falls down in at least one of the categories indicated above) Solutions to problems Missing important steps for solving the problem Initial steps correct but mistakes towards final result P9 P a g e

10 9 Learning and Teaching Expectations: In addition to the above expectations, students should get expertise in any of the multi-paradigm numerical computing environment and fourth generation programming languages like Mathlab. Developing any system requires integrating mechanical, electrical, control and embedded software subsystems. It is expected that this module would enable the students to design and simulate all of these domains in a single environment. At the end of the course, students must be able to understand and manage complex systems interactions. Further, be able to detect design inefficiencies and errors during early development of systems using predict and optimization techniques. 10. CCE Graduate Attributes P10 P a g e

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