BMC401: Applied Mathematics – IV Syllabus for BM 4th Sem 2017 Pattern Mumbai University

Applied Mathematics – IV detailed syllabus scheme for Biomedical Engineering (BM), 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 Biomedical Engineering 4th Sem Syllabus 2017 Pattern, do visit BM 4th Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics – iv is as follows.

Applied Mathematics – IV Syllabus for Biomedical Engineering SE 4th Sem 2017 Pattern Mumbai University

Course Objectives:

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Course Outcomes:

• It is expected that learner will develop the proactive approach towards the selection of methods to a solution of Biomedical Engineering problems.
• Learner will be able identify different probability distribution , learn sampling technique, compute Eigen values and Eigen vectors and evaluate complex integrals and use their application in Biomedical Engineering problems.
• Learner will be able to know new subjects that are required to solve in industry.

Module 1

Calculus of Variation: 06

1. Eulers Langrange equation, solution of Eulers Langrange equation (only results for different cases for Function) independent of a variable, independent of another variable, independent of differentiation of a variable and independent of both variables
2. Isoperimetric problems, several dependent variables
3. Functions involving higher order derivatives: Rayleigh-Ritz method

Module 2

Linear Algebra: Vector Spaces 06

1. Vectors in n-dimensional vector space: properties, dot product, cross product, norm and distance properties in n-dimensional vector space.
2. Vector spaces over real field, properties of vector spaces over real field, subspaces.
3. The Cauchy-Schwarz inequality, Orthogonal Subspaces, Gram-Schmidt process.

Module 3

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Module 4

Probability 10

1. Bayes Theorem (without proof.
2. Random variable: Probability distribution for discrete and continuous random variables, Density function and distribution function, expectation, variance.
3. Moments, Moment Generating Function.
4. Probability distribution: Binomial distribution, Poisson & normal distribution (For detailed study.

Module 5

Correlation 04

1. Karl Pearsons coefficient of correlation, Covariance, Spearmans Rank correlation,
2. Lines of Regression.

Module 6

Complex integration 12

1. Complex Integration: Line Integral, Cauchys Integral theorem for simply connected regions, Cauchys Integral formula.
2. Taylors and Laurents Series
3. Zeros, singularities, poles of f(z), residues, Cauchys Residue theorem.
4. Applications of Residue theorem to evaluate real Integrals of different types.

Text Books:

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.
.

Reference Books:

1. B. V. Ramana, Higher Engineering Mathematics, Tata Mc-Graw Hill Publication
2. Wylie and Barret, Advanced Engineering Mathematics, Tata Mc-Graw Hill 6th Edition
3. Erwin Kreysizg, Advanced Engineering Mathematics, John Wiley & Sons, Inc
4. Seymour Lipschutz Beginning Linear Algebra Schaums outline series, Mc-Graw Hill Publication
5. Seymour Lipschutz Probability Schaums outline series, Mc-Graw Hill Publication

Assessment:

Internal Assessment consists of two tests out of which; one should be compulsory class test (on minimum 02 Modules) and the other is either a class test or assignment on live problems or course project. Term Work: Term work shall consist of minimum 8 tutorials The distribution of marks for term work shall be as follows: Tutorials : 20 Marks Attendance : 5 Marks The final certification and acceptance of term work ensures the satisfactory performance of laboratory work and minimum passing in the term work.

Theory Examination:

1. Question paper will comprise of 6 questions, each carrying 20 marks.
2. Total four questions need to be solved.
3. 1 will be compulsory, based on entire syllabus wherein sub questions of 2 to 5 marks will be asked 4: Remaining question will be randomly selected from all the modules.

For detail syllabus of all other subjects of Biomedical Engineering (BM) 4th Sem 2017 regulation, visit BM 4th Sem Subjects syllabus for 2017 regulation.