Applied Mathematics (Mechanical Engineering)
Self enrolment

 

Class & Semester

:

 S. Y. B. Tech. (Mechanical Engineering)   Part II, Semester  IV

 

Course Title

:

APPLIED  MATHEMATICS

Course Code: 

:

ME221

 

Course Objectives:

1.      To describe solution of LDE and its applications in mechanical engineering.

2.      To introduce Partial Differential Equations and its Applications.

3.      To introduce  Laplace Transform & Inverse Laplace transform  and its Applications.

4.      To explain Vector Differentiation and Vector Integration

5.      The student must be able to formulate a mathematical model of a real life and engineering problem, solve and interpret the solution in real world.

Course Outcomes:

At the end of course student will able to

  1. Solve Linear Differential Equations and Apply them to realistic problems.
  2. Solve Partial Differential Equations for solving problems in Mechanical Engineering fields.
  3. Understand Application of Laplace Transform in Mechanical Engineering
  4. Apply knowledge of Vector Calculus to solve engineering problems.

 

Curriculum Content

Hours

Unit I: Linear Differential Equations

Linear Differential Equations with constant coefficients, Homogenous Linear differential equations, method of variation of parameters.

 

Unit II: Applications of Linear Differential Equations

Applications of Linear Differential Equations with constant coefficients to Whirling of shafts and oscillations of a spring (Free oscillations, Damped oscillations, Forced oscillations without damping)

 

Unit III: Partial Differential Equations

Four standard forms of partial differential equations of first order.

 

Unit IV: Applications of Partial Differential Equations

Wave Equation, One and two dimensional heat flow equations, method of separation of variables, use of Fourier series.

 

Unit V: Laplace Transform

Definition, L.T. of standard functions, Properties and theorems of Laplace transforms, Inverse L.T., Applications of L.T. to solve LDE (Initial value problems)

 

Unit VI: Vector Calculus

Vector Differentiation: Differentiation of vectors, Gradient of scalar point function, Directional derivative, Divergence of vector point function, Curl of a vector point function. Solenoidal, Irrotational and Conservative field. Vector Integration: The line integral, Surface integral, volume integral, Gauss’s Divergence theorem, Stoke’s theorem, Green’s theorem (Without proof).

 

Suggested list of Tutorials/Assignments-

1.      To find solution of LDE with constant coefficients

2.      To find Solution of Homogeneous LDE

3.      Applications of LDE

4.      To find solution of PDE

5.      Applications Of PDE

6.      Laplace Transform

7.      Applications of Laplace transform

8.      Vector differentiation

9.      Vector Integration

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 solve engineering mathematics  problems  using different software’s  in tutorial class only.

3.      Each Student has to write at least 6 assignments on entire syllabus.

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Text Books

 

1.      Erwin Kreyszig, “Advanced Engineering Mathematics (7th Edition)”, Wiley Eastern Ltd., Bombay.

Reference Books

 

1.      B. S. Grewal, “Higher Engineering Mathematics”, Khanna Publications, New Delhi.

2.      C.R.Wylie, “Advanced Engineering Mathematics”, McGraw Hill Publication, New Delhi.

3.      Merle C. Potter, “Advanced Engineering Mathematics”, OXFORD University Press, 3rd Edition

4.      P. N. Wartikar and J. N. Wartikar, “A Text Book of Engineering Mathematics (Volume-I ,II & II)”, Pune Vidyarthi Griha Prakashan, Pune.

5.      Shanti Narayan, “Differential Calculus” S. Chand and company, New Delhi.

6.      S. S. Sastry, “Engineering Mathematics (Volume-I)”, Prentice Hall Publication, New Delhi.

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

8.      M. D. Greenberg, “Advanced  Engineering Mathematics”, Pearson Education.

9.      H. K. Das, “Advanced Engineering Mathematics”, S. Chand Publication.