Applied Mathematics-IV detailed syllabus scheme for Civil Engineering (CE), 2017 regulation has been taken from the University of Mumbai official website and presented for the Bachelor of Engineering students. For Course Code, Course Title, Test 1, Test 2, Avg, End Sem Exam, Team Work, Practical, Oral, Total, and other information, do visit full semester subjects post given below.
For all other Mumbai University Civil Engineering 4th Sem Syllabus 2017 Pattern, do visit CE 4th Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics-iv is as follows.
Applied Mathematics-IV Syllabus for Civil Engineering SE 4th Sem 2017 Pattern Mumbai University
Rationale
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Course Objectives:
- To inculcate an ability to relate engineering problems to mathematical context.
- To provide a solid foundation in mathematical fundamentals required to solve engineering problem.
- To study the basic principles of Vector analyses, complex integration, probability, test of hypothesis and correlation between data.
Module I
- Matrices 11
- Brief revision of vectors over a real field, inner product, norm, Linear dependence and Independence and orthogonality of vectors.
- Characteristic polynomial, characteristic equation, characteristic roots and characteristic vectors of a square matrix, properties of characteristic roots and Eigen vectors of different types of matrices such as symmetric matrix, orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix.
- Cayley Hamilton theorem (without proof) and its application
- Similarity of matrices, Functions of a square matrix, Minimal polynomial and Derogatory matrix.
- Quadratic forms: linear transformation of a quadratic form, congruence of a square matrix, reduction to canonical form under congruent transformations, orthogonal transformation, determining the nature of a quadratic form, Application of Eigen values and Eigen Vectors.
Module II
Vector calculus 9
- Brief revision of Scalar and vector point functions, Gradient, divergence and curl, Irrotational vectors, scalar potential, solenoidal vectors, Directional derivatives.
- Line integrals, Circulation, Greens theorem (without proof) for plane regions and properties of line integrals.
- Surface integrals, Stokes theorem(without proof.
- Volume integrals, Gauss divergence theorem (without proof) related identities and deductions. (No verification problems on Stokes Theorem and Gauss Divergence Theorem.
Module III
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Module IV
Non Linear Programming 06
- Unconstrained optimization, problems with equality constraints, Lagranges Multiplier method
- Problem with inequality constraints Kuhn-Tucker conditions.
Module V
Probability Distributions 10
- Discrete and Continuous random variables, Probability mass and density function, Probability distribution for random variables, Expected value, Variance.
- Probability distributions: Binomial, Poisson, Normal and exponential Distributions.
Module VI
Sampling Theory 08
- Sampling distribution, Test of Hypothesis, Level of significance, critical region, One tailed and two tailed tests Interval Estimation of population parameters.
- Test of significance for Large samples: Test for significance of the difference between sample mean and population means, Test for significance of the difference between the means of two samples.
- Test of significance of small samples:-Students t-distribution and its properties. Test for significance of the difference between sample mean and population mean, Test for significance of the difference between the means of two Samples, paired t-test.
- Chi square test, Test of goodness of fit and independence of attributes, Contingency table and Yates correction.
- Analysis of Variance(F-Test): One way classification, Two-way classification (short-cut method.
Course Outcomes:
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Theory examination:
- The question paper will comprise of six questions; each carrying 20 marks.
- The first question will be compulsory and will have short questions having weightage of 4 – 5marks covering the entire syllabus.
- The remaining five questions will be based on all the modules of the entire syllabus and may before this, the modules shall be divided proportionately and further, the weightage of the marks shall be judiciously awarded in proportion to the importance of the sub-module and contents thereof.
- Remaining questions will be mixed in nature (e.g. Suppose Q.2 has part
- from module II then part
- will be from any module other than module II).
- The students will have to attempt any three questions out of remaining five questions.
- Total four questions need to be attempted.
Internal Assessment:
There will be two class tests (to be referred to as an Internal Assessment) to be conducted in the semester. The first internal assessment (IA) will be conducted in the mid of the semester based on the 40% of the syllabus. It will be of 20 marks. Similarly, the second internal assessment (IA) will be conducted at the end of the semester and it will be based on next 40% of the syllabus. It will be of 20 marks. Lastly, the average of the marks scored by the students in both the Internal Assessment will be considered. Duration of both the IA examination will be of one hour duration, respectively.
Term Work Examination:
The marks of term-work shall be judiciously awarded depending upon the quality of the term work including that of the report on experiments assignments. The final certification acceptance of term-work warrants the satisfactory the appropriate completion of the assignments the minimum passing marks to be obtained by the students. Broadly, the split of the marks for term work shall be as given below. However, there can be further bifurcation in the marks under any of the heads to account for any sub-head therein. Assignments (02) on entire syllabus : 05 marks Class Tutorials on entire syllabus (08. : 15 marks Attendance (Theory and Tutorial. : 05 marks Total : 25 marks Further, while giving weightage of marks on the attendance, following guidelines shall be resorted to. 75% – 80%: 03 Marks; 81% – 90%: 04 Marks 91% onwards: 05 Marks
General Instructions:
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Recommended Books:
- Advanced Engineering Mathematics, E Kreyszing, Wiley Eastern Limited.
- Higher Engineering Mathematics, B. S. Grewal, Khanna Publication.
- Advanced Engineering Mathematics, H. K. Dass, S. Chand & co.
- Vector Analysis by Murray R. Spiegel, Shaum Series.
- Operations Research, S.D. Sharma, S. Chand & CO.
- Fundamentals of Mathematical Statistics, S C Gupta & V K Kapoor, S. Chand & Co
For detail syllabus of all other subjects of Civil Engineering (CE) 4th Sem 2017 regulation, visit CE 4th Sem Subjects syllabus for 2017 regulation.