Applied Mathematics – III detailed syllabus scheme for Civil Engineering (CE), 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 Civil Engineering 3rd Sem Syllabus 2017 Pattern, do visit CE 3rd Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics – iii is as follows.
Applied Mathematics – III Syllabus for Civil Engineering SE 3rd Sem 2017 Pattern Mumbai University
Rationale
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Course Objectives:
- To provide sound foundation in the mathematical fundamentals necessary to formulate, solve and analyse engineering problems.
- To study the basic principles of Laplace Transform, Fourier series, Complex variables
Module I
Laplace Transform 12
- Function of bounded variation, Laplace Transform of standard functions such as 1, tn, eat, sin at, cos at, sinh at, cosh at .
- 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) Heaviside Unit step function, Direct Delta function, Periodic functions and their Laplace Transform.
- Inverse Laplace Transform: Linearity property, use of theorems to find inverse Laplace Transform, Partial fractions method and convolution theorem.
- Applications to solve initial and boundary value problems involving ordinary Differential equations with one dependent variable.
Module II
Complex variables 08
- Functions of complex variable, Analytic function, necessary and sufficient conditions for f z to be analytic (without proof), Cauchy-Riemann equations in polar coordinates.
- Milne-Thomson method to determine analytic function f z when its real or imaginary or its combination is given. Harmonic function, orthogonal trajectories.
- Mapping: Conformal mapping, standard transformations such as translation, rotation and magnification, inversion and reflection, linear transformation, bilinear transformation, cross ratio, fixed points.
Module III
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Module IV
Fourier Series 09
- Orthogonal and orthonormal functions, Construction of orthonormal set.
- Dirichlet conditions. Fourier series of periodic function with period 2 &2l .Fourier series of even and odd functions, Half range sine and cosine series
- Parsevals identities (without proof.
- Complex form of Fourier series.
Module V
Partial Differential Equations 08
- Classification of partial differential equations of second order, Heat equation, Wave equation, Laplace equation,
- Method of Separation of variables, Solution of one dimensional heat conduction equation, steady state configuration for heat flow, solution of one dimensional wave equation, transverse vibrations of an elastic string, Laplace equation in rectangular region, Use of Fourier series and applications of Laplace transform in solving these equations.
- Numerical Solution of Partial differential equations using Bender-Schmidt Explicit Method and simplified Crank- Nicolson implicit method.
Module VI
- Correlation and Regression. 06
- Correlation, Co-variance, Karl Pearson Coefficient of Correlation and Spearmans Rank Correlation Coefficient (non-repeated and repeated ranks.
- Regression Coefficients and lines of regression
- 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.
Course Outcomes:
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Theory examination:
- The question paper will comprise of six questions; each carrying 20 marks.
- The first question will be compulsory and will have short questions having weightage of 4 – 5marks covering the entire syllabus.
- The remaining five questions will be based on all the modules of the entire syllabus and may before this, the modules shall be divided proportionately and further, the weightage of the marks shall be judiciously awarded in proportion to the importance of the sub-module and contents thereof.
- Remaining questions will be mixed in nature (e.g. Suppose Q.2 has part
- from module II then part
- will be from any module other than module II).
- The students will have to attempt any three questions out of remaining five questions.
- Total four questions need to be attempted.
Internal Assessment:
There will be two class tests (to be referred to as an Internal Assessment) to be conducted in the semester. The first internal assessment (IA) will be conducted in the mid of the semester based on the 40% of the syllabus. It will be of 20 marks. Similarly, the second internal assessment (IA) will be conducted at the end of the semester and it will be based on next 40% of the syllabus. It will be of 20 marks. Lastly, the average of the marks scored by the students in both the Internal Assessment will be considered. Duration of both the IA examination will be of one hour duration, respectively.
Term Work Examination:
The marks of term-work shall be judiciously awarded depending upon the quality of the term work including that of the report on experiments assignments. The final certification acceptance of term-work warrants the satisfactory the appropriate completion of the assignments the minimum passing marks to be obtained by the students. Broadly, the split of the marks for term work shall be as given below. However, there can be further bifurcation in the marks under any of the heads to account for any sub-head therein. Assignments (02) on entire syllabus : 05 marks Class Tutorials on entire syllabus (08. : 15 marks Attendance (Theory and Tutorial. : 05 marks Total : 25 marks Further, while giving weightage of marks on the attendance, following guidelines shall be resorted to. 75% – 80%: 03 Marks; 81% – 90%: 04 Marks 91% onwards: 05 Marks
General Instructions:
For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
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Recommended Books:
- Higher Engineering Mathematics, Dr B. S. Grewal, Khanna Publication.
- Advanced Engineering Mathematics, E Kreyszing, Wiley Eastern Limited.
- Higher Engineering Mathematics, B.V. Ramana, McGraw Hill Education, New Delhi.
- Complex Variables: Churchill, Mc-Graw Hill.
- Integral Transforms and their Engineering Applications, Dr B. B. Singh, Synergy Knowledgeware, Mumbai.
- Numerical Methods, Kandasamy, S. Chand & CO.
For detail syllabus of all other subjects of Civil Engineering (CE) 3rd Sem 2017 regulation, visit CE 3rd Sem Subjects syllabus for 2017 regulation.