AEC301: Applied Mathematics III Syllabus for AE 3rd Sem 2017 Pattern Mumbai University

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

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

Course Outcomes:

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Module 1

Laplace Transform

1. Function of bounded variation, Laplace Transform of standard functions such as 1, t^n, e^at, 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 text 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 f z to be analytic (without proof), Cauchy-Riemann equations in polar coordinates.
2. Milne- Thomson method to determine analytic function f z 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

Complex Integration

1. Line integral of a function of a complex variable, Cauchys theorem for analytic functions(without proof)Cauchys integral formula (without proof))Singularities and poles:
2. Taylors and Laurents series development (without proof)
3. Residue at isolated singularity and its evaluation
4. Residue theorem, application to evaluate real integral of type (Follow the text from pdf)

Module 4

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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 = ax2 + bx + c and y = aebx

Assessment:

Internal Assessment for 20 marks: Consisting Two Compulsory Class Tests First test based on approximately 40% of contents and second test based on remaining contents (approximately 40% but excluding contents covered in Test I) End Semester Examination: Weightage of each module in end semester examination will be proportional to number of respective lecture hours mentioned in the curriculum.

1. Question paper will comprise of total six questions, each carrying 20 marks
2. Question 1 will be compulsory and should cover maximum contents of the curriculum
3. Remaining questions will be mixed in nature (for example if Q.2 has part
   1. from module 3 then part
   2. will be from any module other than module 3)
4. Only Four questions need to be solved.

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