PEC301: Applied Mathematics – III Syllabus for PE 3rd Sem 2017 Pattern Mumbai University

Applied Mathematics – III detailed syllabus scheme for Production Engineering (PE), 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 Production Engineering 3rd Sem Syllabus 2017 Pattern, do visit PE 3rd Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics – iii is as follows.

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

Course Objectives:

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Course Outcomes:

Learner will be able to..

1. Demonstrate the ability of using Laplace Transform in solving the Ordinary Differential Equations and Partial Differential Equations
2. Demonstrate the ability of using Fourier Series in solving the Ordinary Differential Equations and Partial Differential Equations
3. Solve initial and boundary value problems involving ordinary differential equations
4. Identify the analytic function, harmonic function, orthogonal trajectories
5. Apply bilinear transformations and conformal mappings
6. Identify the applicability of theorems and evaluate the contour integrals.

Module 1

Laplace Transform

1. Function of bounded variation, Laplace Transform of standard functions such as 1, tn, eat, sin at, cos at, sinh at, cosh at
2. Linearity property of Laplace Transform, First Shifting property, Second Shifting property, Change of Scale property of L.T. (without proof) (follow the equation from pdf) Laplace Transform. of Periodic functions.
3. Inverse Laplace Transform: Linearity property, use of theorems to find inverse Laplace Transform, Partial fractions method and convolution theorem(without proof).
4. Applications to solve initial and boundary value problems involving ordinary differential equations with one dependent variable 12

Module 2

Complex variables:

1. Functions of complex variable, Analytic function, necessary and sufficient conditions fo fz to be analytic (without proof), Cauchy-Riemann equations in polar coordinates.
2. Milne- Thomson method to determine analytic function fz when its real or imaginary or its combination is given. Harmonic function, orthogonal trajectories
3. Mapping: Conformal mapping, linear, bilinear mapping, cross ratio, fixed points and standard transformations such as Rotation and magnification, inversion and reflection, translation 08

Module 3

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Module 4

Fourier Series:

1. Orthogonal and orthonormal functions, Expressions of a function in a series of orthogonal functions. Dirichlets conditions. Fourier series of periodic function with period 2n and 2l
2. Dirichlets theorem(only statement), even and odd functions, Half range sine and cosine series,Parsvels identities (without proof)
3. Complex form of Fourier series 10

Module 5

Partial Differential Equations:

1. Numerical Solution of Partial differential equations using Bender-Schmidt Explicit Method, Implicit method (Crank- Nicolson method).
2. Partial differential equations governing transverse vibrations of an elastic string its solution using Fourier series.
3. Heat equation, steady-state configuration for heat flow
4. Two and Three dimensional Laplace equations 09

Module 6

Correlation and curve fitting

1. Correlation-Karl Pearsons coefficient of correlation- problems, Spearmans Rank correlation problems, Regression analysis- lines of regression (without proof) -problems
2. Curve Fitting: Curve fitting by the method of least squares- fitting of the curves of the form, y = ax + b, y = ax1 2 3 4 5 6 7 + bx + c and y = aebx 05

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.
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Reference Books:

1. Higher Engineering Mathematics, Dr B. S. Grewal, Khanna Publication
2. Advanced Engineering Mathematics, E Kreyszing, Wiley Eastern Limited
3. Higher Engineering Mathematics, B.V. Ramana, McGraw Hill Education, New Delhi
4. Complex Variables: Churchill, Mc-Graw Hill
5. Integral Transforms and their Engineering Applications, Dr B. B. Singh, Synergy Knowledgeware, Mumbai
6. Numerical Methods, Kandasamy, S. Chand & CO
7. Fundamentals of mathematical Statistics by S.C. Gupta and Kapoor

For detail syllabus of all other subjects of Production Engineering (PE) 3rd Sem 2017 regulation, visit PE 3rd Sem Subjects syllabus for 2017 regulation.