FEC101: Engineering Mathematics-I Syllabus for BM 1st Sem 2016 Pattern Mumbai University

Engineering Mathematics-I detailed syllabus scheme for Biomedical Engineering (BM), 2016 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 1st Sem Syllabus 2016 Pattern, do visit BM 1st Sem 2016 Pattern Scheme. The detailed syllabus scheme for engineering mathematics-i is as follows.

Engineering Mathematics-I Syllabus for Biomedical Engineering 1st Year 1st Sem 2016 Pattern Mumbai University

Course Objectives:

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Course Outcomes:

Students will be able to

1. Apply the basic concepts of Complex Numbers and will be able to use it for engineering problems.
2. Apply hyperbolic functions and logarithms in the subjects like electrical circuits, Electromagnetic wave theory.
3. Apply the basic concepts of partial differentiation of function of several variables and will be able to use in subjects like Electromagnetic Theory, Heat and Mass Transfer etc.
4. Apply the concept of Maxima, Minima and Successive differentiation and will be able to use it for optimization and tuning the systems.
5. Apply the concept of Matrices and will be able to use it for solving the KVL and KCL in electrical networks.
6. Apply the concept of Numerical Methods for solving the engineering problems with the help of SCILAB software.

01. Complex Numbers

-Pre-requisite: Review of Complex Numbers-Algebra of Complex Number, Cartesian, polai and exponential form of complex number.

1. Statement of DMoivres Theorem.
2. Expansion of sinn0, cosn0 in terms of sines and cosines of multiplesof 0 and Expansion of sinn0, cosn0 in powers of sin0, cos0
3. Powers and Roots of complex number.

02. Hyperbolic function and Logarithm of Complex Numbers

1. Circular functions of complex number and Hyperbolic functions. Inverse Circular and Inverse Hyperbolic functions. Separation of real and imaginary parts of all types of Functions.
2. Logarithmic functions, Separation of real and Imaginary parts of Logarithmic Functions.# Self learning topics:Applications of complex number in Electrical circuits.

03. Partial Differentiation

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04. Applications of Partial Differentiation and Successive differentiation.

1. Maxima and Minima of a function of two independent variables, Lagranges method of undetermined multipliers with one constraint.
2. Successive differentiation: nth derivative of standard functions. Leibnitzs Theorem (without proof) and problems # Self learning topics: Jacobians of two and three independent variables (simple problems) 3 3

05. Matrices

-Pre-requisite: Inverse of a matrix, addition, multiplication and transpose of a matrix

1. Types of Matrices (symmetric, skew- symmetric, Hermitian, Skew Hermitian, Unitary, Orthogonal Matrices and properties of Matrices). Rank of a Matrix using Echelon forms, reduction to normal form and PAQ form.
2. System of homogeneous and non -homogeneous equations, their consistency and solutions.# Self learning topics:Application of inverse of a matrix to coding theory. 4 2

06. Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function.

1. Solution of Transcendental Equations: Solution by Newton Raphson method and Regula -Falsi method.
2. Solution of system of linear algebraic equations, by
   1. Gauss Jacobi Iteration Method,
   2. Gauss Seidal Iteration Method.
3. Taylors Theorem (Statement only) and Taylors series, Maclaurins series (Statement only). Expansion ofex sin(‘x’), cos(‘x’), tan(‘x’), sinh(‘x’), cosh(‘x’), tanh(‘x’), log(‘1+x’),sin-1(‘x’),cos-1(‘x’),tan-1(‘x’).# Self learning topics: Indeterminate forms, L- Hospital Rule, Gauss Elimination Method, Gauss Jordan Method.

Term Work:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Assessment:

Internal Assessment Test: Assessment consists of two class tests of 20 marks each. The first class test is to be conducted when approx. 40% syllabus is completed and second class test when additional 35% syllabus is completed. Duration of each test shall be one hour. End Semester Theory Examination:

1. Question paper will comprise of total 06 questions, each carrying 20 marks.
2. Total 04 questions need to be solved.
3. Question No: 01 will be compulsory and based on entire syllabus wherein 4sub-questions of 5 marks each will be asked.
4. Remaining questions will be randomly selected from all the modules.
5. Weightage of each module will be proportional to number of respective lecture hoursas mentioned in the syllabus.

Reference Books:

1. Higher Engineering Mathematics, Dr.B.S.Grewal, Khanna Publication
2. Advanced Engineering Mathematics, Erwin Kreyszig, Wiley EasternLimited, 9thEd.
3. Engineering Mathematics by Srimanta Pal and Subodh,C.Bhunia, Oxford University Press
4. Matrices, Shanti Narayan, .S. Chand publication.
5. Applied Numerical Methods with MATLABfor Engineers and Scientists by Steven Chapra, McGraw Hill
6. Elementary Linear Algebra with Application by Howard Anton and Christ Rorres. 6th edition.

For detail syllabus of all other subjects of Biomedical Engineering (BM) 1st Sem 2016 regulation, visit BM 1st Sem Subjects syllabus for 2016 regulation.