Applied Mathematics IV detailed syllabus scheme for Mechanical Engineering (ME), 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 Mechanical Engineering 4th Sem Syllabus 2017 Pattern, do visit ME 4th Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics iv is as follows.
Applied Mathematics IV Syllabus for Mechanical Engineering SE 4th Sem 2017 Pattern Mumbai University
Course Objectives:
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Course Outcomes:
Learner will be able to
- Solve the system of linear equations using matrix algebra with its specific rules
- Demonstrate basics of vector calculus
- Apply the concept of probability distribution and sampling theory to engineering problems
- Apply principles of vector calculus to the analysis of engineering problems
- Identify, formulate and solve engineering problems
- Illustrate basic theory of correlations and regression
Module 1
Matrices:
- Brief revision of vectors over a real field, inner product, norm of a vector
- Eigen values and Eigen vectors: Characteristic polynomial, characteristic equation, characteristic roots and characteristic vectors of a square matrix, properties of characteristic roots and vectors of different types of matrices such as orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix, Cayley Hamilton theorem ( without proof) . Similarity of matrices. Functions of a square matrix 08
Module 2
Matrices:
- Minimal polynomial and Derogatory matrix
- Quadratic forms: Linear transformations of a quadratic form, congruence of a square matrix, reduction to Canonical form under congruent transformations, orthogonal transformations, determining the nature of a quadratic form, Applications of Eigen Values and Eigen Vectors Vector calculus
- Brief revision of Scalar and vector point functions. Gradient of a scalar function, Divergence and curl of a vector function
- Line integrals, circulation of a vector, condition for independence of the path in the line integral 09
Module 3
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Module 4
Linear Programming problems Probability Distributions:
- Big M method (Penalty method) to solve L.P.P, Duality, Dual simplex method and Revised simplex method to solve L.P.P. Probability Distributions
- Discrete and Continuous random variables, Probability mass and density function, Probability distribution for random variables, Expected value, Variance.
- Probability Distributions: Binomial, Poisson and Normal Distributions 09
Module 5
Sampling theory:
- Sampling theory: Sampling distribution. Test of Hypothesis. Level of significance, critical
- region. One tailed and two tailed tests. Interval Estimation of population parameters. Large and small samples
- 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.
- Students t-distribution and its properties. Test of significance of small 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, paired t-test 09
Module 6
Sampling theory and ANOVA
- Chi-square test, Test for the Goodness of fit , Association of attributes and Yates correction
- Analysis of Variance(F-Test): One way classification, Two-way classification(short-cut method. 08
Assessment:
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdf platform to make students’s lives easier..
End Semester Examination:
Weightage of each module in end semester examination will be proportional to number of respective lecture hours mentioned in the curriculum.
- Question paper will comprise of total six questions, each carrying 20 marks
- Question 1 will be compulsory and should cover maximum contents of the curriculum
- Remaining questions will be mixed in nature (for example if Q.2 has part
- from module 3 then part
- will be from any module other than module 3 )
- Only Four questions need to be solved.
Reference 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
- Elements of Applied mathematics, P N & J N Wartikar, Pune Vidyarthi Gruha Prakashan
- Advanced Engineering Mathematics, E Kreyszing, Wiley Eastern Limited
- Operations Research, Kantiswearup, Manmohan, P K Gupta, S. Chand & CO
For detail syllabus of all other subjects of Mechanical Engineering (ME) 4th Sem 2017 regulation, visit ME 4th Sem Subjects syllabus for 2017 regulation.