Course info

Shivaji University, Kolhapur

First Year B. Tech

ENGINEERING MATHEMATICS - II

Teaching Scheme : L : 4 hrs/week

                                   : T: 1 hrs/week                                                                                                         Credits: 5

Evaluation Scheme:   CIE               SEE                                                                         Minimum Passing Marks

                                     (25 + 25)          50                                                                                                      40

Course Objective

1.       To teach Mathematical methodologies and models.

2.       To develop mathematical skills and enhance logical thinking power of students.

3.       To provide students with skills in differential equations, integral calculus  & complex variable which would enable them to devise engineering solutions for given situations they may encounter in their profession.

4.       To produce graduates with mathematical knowledge, computational skills and the ability to deploy these skills effectively in the solution of problems, principally in the area of engineering.

Course Outcome

1.       Students in this course will apply the Procedure and methods to solve technical problems.

2.       Student can understand how to model real world scenario using Mathematics

3.       Students will be able to solve computational problems using Scilab/Matlab

Unit 1 Differential Equations of first order and first degree and its Applications                     8hrs                                                                                         

Exact differential equations, Equations reducible to exact equations, Linear equations, Equations reducible to Linear form, Applications to Orthogonal trajectories and to Simple Electrical Circuits.

Unit 2 Numerical solutions of  Differential Equations of first order and first degree               8hrs                                                                                                              

Taylor's series method , Picard’s method,  Euler's method , Modified Euler's method, Runge-Kutta fourth order formula

Unit 3 Curve Tracing and Rectification                                                                                                          8hrs

Tracing of curves (Cartesian and Polar), Rectification of plane curves (Cartesian and Polar for m)

Unit 4 Integral Calculus                                                                                                                                        8hrs

Beta and Gamma functions, differentiation under the sign of integration, error function.

Unit 5 Multiple Integrals & Applications                                                                                                        8hrs

Introduction of Double Integrals, Evaluation of Double Integrals, Change of order of Integration, Change of variables using Jacobians, Change to Polar, Evaluation of Triple Integral with given limits. Applications Of Multiple Integrals: Area enclosed by plane curves, Mass of plane Lamina and volumes of solid.

 Unit 6 Complex variables                                                                                                                                   8hrs

Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series and Residue theorem.

Suggested list of Tutorials/Assignments-

1.       Exact differential Equations

2.       Linear differential equations

3.       Numerical solutions of ODEs

4.       Curve tracing

5.       Rectification

6.       Integral calculus

7.       Double  and Triple Integration

8.       Applications of Multiple integrals

9.       Cauchy’s Integral theorem and Cauchy’s integral formula

10.   Taylor series and Laurent series

11.   Residue theorem

12.   Introduction to scilab/Matlab

General Instructions:

1.       Batch wise tutorials are to be conducted. The number of students per batch should be as per the practical batches.

2.       Students must be encouraged to write Scilab/Matlab Programs in tutorial class only. Each Student has to write at least 4 Scilab tutorials (including print out) and at least 6 class tutorials on entire syllabus.

3.       Scilab/Matlab Tutorials will be based on

1.       Numerical solutions of differential equations of first order and first degree

2.       Tracing Curves in Scilab/Matlab

3.       Evaluation of single integral in Scilab/Matlab

4.       Double and triple integral in Scilab/Matlab

5.       Complex variable in Scilab/Matlab

Reference Books-

1.    Dr. B. S. Grewal , “Higher Engineering Mathematics,” - Khanna Publishers, Delhi.

2.    Erwin Kreyszig, “Advanced Engineering Mathematics”, - New Age International (P) Ltd. Publishers.

3.    H K Dass, “Advanced Engineering Mathematics”,  S. Chand Publishing

4.    M. K. Jain, S. R. K. Iyengar, R. K. Jain, “Numerical Methods for Scientific and Engineering Computation”, – New Age International (P) Ltd.

5.    P. N. Wartikar & J. N. Wartikar , “A Text Book of Applied Mathematics Vol.-I and II,” – Pune Vidyarthi Griha Prakashan, Pune.

6.    N.P. Bali and Manish Goyal, "A text book of Engineering Mathematics”, Laxmi Publications, latest edition

7.    B.V. Ramana, “Higher Engineering Mathematics”, Tata McGraw-Hill.