Applied Mathematics-III detailed syllabus scheme for Biotechnology (BT), 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 Biotechnology 3rd Sem Syllabus 2017 Pattern, do visit BT 3rd Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics-iii is as follows.
Applied Mathematics-III Syllabus for Biotechnology SE 3rd Sem 2017 Pattern Mumbai University
Prerequisites:
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Course Objectives:
- To introduce students to the basic methods of Laplace transforms.
- Laplace transforms and inverse Laplace transforms of all the standard functions.
- To enable students to solve initial value ODE problems using L-transforms.
- To study eigen values and eigen spaces of matrices.
- Orthogonal and congruent reduction of quadratic forms.
- Complex analysis: C-R equations, Milne-Thomson method.
- Bilinear transformations and cross-ratios.
- Introduction to statistics.
- Lagrange multiplier method for 2 and 3 variables with no more than two constraints.
- To introduce the basics of optimization using Kuhn-Tucker conditions.
Course Outcomes:
- The student will be able to solve initial value ODE problems.
- The student will have a good understanding of real and complex analysis.
- The student will have a thorough grounding in matrix algebra.
- The student will be ready for any further courses on optimization.
Module 1
The Laplace transform: Definition and properties (without proofs); all standard transform methods for elementary functions including hyperbolic functions; Heaviside unit step function, Dirac delta function; the error function; evaluation of integrals using Laplace transforms; inverse Laplace transforms using partial fractions and H(t-a); convolution (no proof). 07
Module 2
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Module 3
Complex analysis: Cauchy-Riemann equations (only in Cartesian co- ordinates) for an analytic function (no proof); harmonic function; Laplaces equation; harmonic conjugates and orthogonal trajectories (Cartesian co- ordinates); to find fz when u+v or u-v are given; Milne-Thomson method; cross-ratio (no proofs); conformal mappings; images of straight lines and circles.
Module 4
Complex Integration Cauchys integral formula; poles and residues; Cauchys residue theorem; applications to evaluate real integrals of trigonometric functions; integrals in the upper half plane; the argument principle. 06
Module 5
Statistics: (No theory questions expected in this module) Mean, median, variance, standard deviation; binomial, Poisson and normal distributions; correlation and regression between 2 variables. 05
Module 6
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Term work
Term work shall consist of minimum eight tutorials from entire syllabus which are to be given at regular intervals Batch wise. Tutorials: 20 marks Attendance: 05 marks Total: 25 marks
Assessment
Internal:
- Assessment consists of average of two tests which should be conducted at proper interval.
End Semester theory examination
- Question paper will comprise of 6 questions, each carrying 20 marks.
- Total 4 questions need to be solved.
- Question No.1 will be compulsory and based on entire syllabus wherein sub questions can be asked.
- Remaining questions will be randomly selected from all the modules.
- Weightage of marks should be proportional to number of hours assigned to each Module.
Reference Books:
- Mathematical Methods in Chemical Engineering, V.G. Jenson and G.V. Jeffreys, Academic Press, 1970
- Laplace transforms, Murray Spiegel, Schaums Outline Series, 1974
- Complex variables, Murray Spiegel, Schaums Outline Series, 1964
- Linear Algebra, Murray Spiegel, Schaums Outline Series, 1964
- Probability and Statistics: Murray R. Spiegel, Schaum’s Outline Series, 1965
- Advanced Engineering Mathematics by Erwin Kreyszig, 9th Edition, Wiley India.
For detail syllabus of all other subjects of Biotechnology (BT) 3rd Sem 2017 regulation, visit BT 3rd Sem Subjects syllabus for 2017 regulation.