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RAMRAO ADIK INSTITUTE OF TECHNOLOGY NERUL, NAVI MUMBAI Department of Engineering Sciences (Academic Year: - 2014-15) Program :–B. E. (COMPUTER) Name of the course: AM- IV Year : 2015 Semester: IV Name of Faculty : Mrs.Shilpa Bhangale, Mr. Mahadev Zende Academic Year: 2014-15 Course outcomes: CO1 : Students will apply the method of solving complex integration and computing residues also to find contour integrals. CO2 : Demonstrate ability to manipulate matrices and compute eigen values and eigen vectors. CO3 : Students can relate the two different data. CO4: Students will recognize the role of probability theory in the applications of many different fields. CO5: Students will be able to represent and statistically analyze the data both graphically and numerically. CO6: Students will be able to analyze the solution of a linear optimization problem. Program Outcomes: Program outcomes are narrower statements that describe what students are expected to know and be able to do by the time of graduation. These relate to the skills, knowledge, and behaviors. Engineering programs must demonstrate that their students attain the following outcomes: Pa) an ability to apply knowledge of mathematics, science, and engineering, Pb) an ability to design and conduct experiments, as well as to analyze and interpret data, Pc) an ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability, Pd) an ability to function on multidisciplinary teams. Pe) an ability to identify, formulates and s olve engineering problems, Pf) an understanding of professional and ethical responsibility, Pg) an ability to communicate effectively. Ph) the broad education n e c e s s a r y to understand the impact of engineering s o l u t i o n s in a global, economic, environmental, and societal context, Pi) A recognition of the need for, an ability to engage in lifelong learning. Pj) A knowledge of contemporary issues. Pk) an ability to use the techniques, skills, and modern engineering tools necessary for higher studies and engineering practices. Pl) An ability to have leadership and management skills to accomplish a defined goal. Mapping of CO’s with PO’s Subject: Applied Mathematics IV Credits: 5 Course code: CSC401 Course Outcomes (Weightage-60%) Theory Credits: 4 Program Outcomes Pa Pb Pc Pd Pe Pf Pg Ph Pi Pj Pk CO1 2 2 2 CO2 2 2 2 CO3 1 2 2 CO4 2 2 2 CO5 1 2 1 CO6 2 2 2 1 2 Course Outcomes (Weightage-40%) Theory Credit: 1 Pl Program Outcomes Pa Pb Pc Pd Pe Pf Pg Ph Pi Pj Pk CO1 2 1 1 CO2 1 2 1 CO3 1 CO4 1 CO5 1 CO6 1 1 1 2 2 1 1 1 2 1 Pl \ SYLLABUS AM-IV Subject Code Subject Name Teaching Scheme Theo ry SEITC401 Subject Code Applied Mathematics IV * Pract. 04 Credits Assigned Tutorial -- Theory 01 Subject Name Total - 01 05 Examination Scheme Internal assessment Applied Mathematics –IV* Tutorial 04 Theory Marks SEITC401 TW/ Pract. Test1 Test2 20 20 Avg. 20 Term Work Practical Oral Total End Sem. Exam 80 25 - - 125 Detailed Syllabus: Sr.No. Details Module 01 Complex Integration 1.1 Complex Integration – Line Integral, Cauchy’s Integral theorem for simply connected regions, Cauchy’s Integral formula(without proof) 1.2 Taylor’s and Laurent’s series ( without proof) 1.3 Zeros, poles of f(z), Residues, Cauchy’s Residue theorem 1.4 Applications of Residue theorem to evaluate Integrals. Module 02 Module 03 Matrices 2.1 Eigen values and eigen vectors 2.2 Cayley-Hamilton theorem(without proof) 2.3 Similar matrices, diagonalisable of matrix. 2.4 Derogatory and non-derogatory matrices ,functions of square matrix. Correlation Hrs (10) (08) (04) Module 04 Module 05 Module 06 3.1 Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance, Spearman’s Rank correlation. 3.2 Regression Lines. Probability 4.1 Baye’s Theorem, 4.2 Random Variables:- discrete & continuous random variables, expectation, Variance, Probability Density Function & Cumulative Density Function. 4.3 Moments, Moment Generating Function. 4.4 Probability distribution: binomial distribution, Poisson & normal distribution. (For detail study) Sampling theory 5.1 Test of Hypothesis, Level of significance, Critical region, One Tailed and two Tailed test, Test of significant for Large Samples:-Means of the samples and test of significant of means of two large samples. 5.2 Test of significant of small samples:- Students t- distribution for dependent and independent samples. 5.3 Chi square test:- Test of goodness of fit and independence of attributes, Contingency table. Mathematical Programming 6.1 Types of solution, Standard and Canonical form of LPP, Basic and feasible solutions, simplex method. 6.2 Artificial variables, Big –M method (method of penalty). 6.3 Duality, Dual simplex method. 6.4 Non Linear Programming:-Problems with equality constrains and inequality constrains (No formulation, No Graphical method). Term work: Term work shall consist of minimum four SCILAB practicals and six tutorials. SCILAB practicals : 08 marks Tutorials : 12 marks Attendance : 05 marks Total : 25 marks Recommended Books: 1. Higher Engineering Mathematics by Grewal B. S. 38th edition, Khanna Publication 2005. 2. Operation Research by Hira & Gupta,S Chand. 3. A Text Book of Applied Mathematics Vol. I & II by P.N.Wartilar & J.N.Wartikar, Pune, Vidyarthi Griha Prakashan., Pune. 4. Probability and Statistics for Engineering, Dr. J Ravichandran, Wiley-India. 5. Mathematical Statistics by H. C Saxena, S Chand & Co. Reference Books: 1. 2. 3. 4. Advanced Engg. Mathematics by C. Ray Wylie & Louis Barrett.TMH International Edition. Mathematical Methods of Science and Engineering by Kanti B. Datta, Cengage Learning. Advanced Engineering Mathematics by Kreyszig E. 9th edition, John Wiley. Operations Research by S.D. Sharma Kedar Nath, Ram Nath & Co. Meerat. (08) (08) (10) 5. Engineering optimization (Theory and Practice) by Singiresu S.Rao, New Age International publication. 6. Probability by Seymour Lipschutz, McGraw-Hill publication. Theory Examination: Question paper will comprise of 6 questions, each carrying 20 marks. Total 4 questions need to be solved. Q.1 will be compulsory, based on entire syllabus wherein sub questions of 2 to 3 marks will be asked. Remaining question will be randomly selected from all the modules. Weightage of marks should be proportional to number of hours assigned to each module. LECTURE PLAN Lecture no. Dates Modules Course outcomes Module 1 : Complex Integration L-1 Complex integration – Line integral CO1 L-2 Cauchy’s integral theorem for simply connected regions, problems. CO1 L-3 Cauchy’s integral formula, problems CO1 L-4 Problems on above topics CO1 L-5 Taylors series, related problems CO1 L-6 Laurent series, related problems CO1 L-7 Zeros, singularities, poles, residues CO1 L-8 Cauchy’s residue theorem, related problems CO1 L-9 Applications of residue theorem CO1 L-9 Applications of residue theorem CO1 L-10 Problems on above topics CO1 Module 2 : Matrices L-11 Eigen values and eigen vectors CO2 L-12 Problems of eigen values and eigen vectors CO2 L-13 Cayley Hamilton theorem with problems CO2 L-14 Similar matrices, problems CO2 L-15 Diagonalisable of matrix CO2 L-16 Problems on above topics CO2 L-17 Derogatory and non-derogatory matrices CO2 Module 3 : Correlation L-18 Scattered diagrams, Karl Pearson’s coefficient of correlation CO3 L-19 Covariance CO3 L-20 Spearman’s Rank correlation, problems CO3 L-21 Regression Lines CO3 L-22 Problems on above topics CO3 Module 4: Probability L-23 Baye’s Theorem, problems CO4 L-24 Random variables, discrete and continous r.v, expectation CO4 L-25 Variance ,Probability density function and cumulative density function CO4 L-26 Moments, problems based on moments CO4 L--27 Problems on above topics CO4 L-28 Moment generating function CO4 L-29 Probability distribution- Binomial distribution CO4 L-30 Poisson distribution CO4 L-31 Normal distribution CO4 L-32 Problems on above topics CO4 Module 5 : Sampling Theory L-33 Test of hypothesis, level of significance, critical region, one tailed test, two tailed test CO5 L-34 Test of significant for large samples :means of samples CO5 L-35 Test of significant of means of two large samples CO5 L-36 Test of significant of small samples : tdistribution for dependent sample CO5 L-37 t-distribution for independent samples CO5 L-38 Chi-square test : test of goodness of fit CO5 L-39 Test of independence of attributes CO5 L-40 Problems on above topics CO5 Module 6: Mathematical Programming L-41 Types of solution, standard and canonical form of LPP. CO6 L-42 Basic and feasible solutions CO6 L-43 Simplex method CO6 L-44 Artificial variables, Big – M method(method of penalty) CO6 L-45 Duality problems CO6 L-46 Dual simplex method Problems CO6 L-47 Non linear programming problems with equality constraints CO6 L-48 Problems on above topic CO6 L-49 Non linear programming :inequality constraints CO6 L-50 Problems on above topics CO6 LIST OF TUTORIALS AND SCILAB PRACTICALS TUTORIAL NO. 1. 2. 3. 4. 5 6 7. SCILAB PRACTICALS 1. 2. 3. TOPICS Complex integration Matrices Correlation and regression Probability Sampling theory Mathematical programming 1(LPP) Mathematical programming2(NLPP) TOPICS Correlation Binomial distribution Poisson distribution Course outcomes CO1 CO2 CO3 CO4 CO5 CO6 CO6 Course outcomes Co3 Co4 Co4