BMC301: Applied Mathematics III Syllabus for BM 3rd Sem 2017 Pattern Mumbai University

Applied Mathematics III 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 3rd Sem Syllabus 2017 Pattern, do visit BM 3rd Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics iii is as follows.

Applied Mathematics III Syllabus for Biomedical Engineering SE 3rd Sem 2017 Pattern Mumbai University

Course Objectives:

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Course Outcomes:

• Learner will demonstrate basic knowledge of Laplace Transform. Fourier series, Bessel Functions, Vector Algebra and Complex Variable.
• Learner will demonstrate an ability to identify and Model the problems of the field of Biomedical Engineering and solve it.
• Learner will be able to apply the application of Mathematics in Biomedical Engineering.

Module 1

Laplace Transform

1. Laplace Transform (LT) of Standard Functions: Definition of Laplace transform, Condition of Existence of Laplace transform, Laplace transform of e^at, Sin(at),cos(at), sinh(at ),cosh(at), t^n Heaviside unit step function, Dirac-delta function, Laplace transform of Periodic function 7
2. Properties of Laplace Transform: Linearity, first shifting theorem, second shifting theorem, multiplication by tn ,Division by t, Laplace Transform of derivatives and integrals, change of scale, convolution theorem, Evaluation of integrals using Laplace transform.

Module 2

Inverse Laplace Transform & its Applications

1. Partial fraction method, Method of convolution, Laplace inverse by derivative 6
2. Applications of Laplace Transform: Solution of ordinary differential equations, Solving RLC circuit differential equation of first order and second order with boundary condition using Laplace transform (framing of differential equation is not included.

Module 3

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Module 4

1. Vector Algebra & Vector Differentiation
2. Review of Scalar and Vector Product: Scalar and vector product of three and four vectors, Vector differentiation, Gradient of scalar point function, Divergence and Curl of vector point function 7
3. Properties: Solenoidal and irrotational vector fields, conservative vector field

Module 5

1. Vector Integral
2. Line integral 6
3. Greens theorem in a plane, Gauss divergence theorem and Stokes theorem

Module 6

1. Complex Variable & Bessel Functions
2. Analytic Function: Necessary and sufficient conditions (No Proof), Cauchy Reiman equation Cartesian form (No Proof) Cauchy Reiman Equation in polar form (with Proof), Milne Thomson Method and it application, Harmonic function, orthogonal trajectories 11
3. Mapping: Conformal mapping, Bilinear transformations, cross ratio, fixed points
4. Bessel Functions: Bessels differential equation, Properties of Bessel function of order +1/2 and -1/2, Generating function, expression of cos (xsni”), sin (x sin#) in term of Bessel functions

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.
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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. Murry R. Spieget, VectorAnalysis, 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 eight tutorials and assignments (minimum 2). The distribution of marks for term work shall be as follows: Tutorials :15 marks Assignments :05 marks Attendance (Theory and Tutorial. :05 marks The final certification and acceptance of term work ensures 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. Q.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) 3rd Sem 2017 regulation, visit BM 3rd Sem Subjects syllabus for 2017 regulation.