Sem - IV (Second Year)

COURSE OUTCOMES

CO1.   Describing various methods of solving differential equations, partial differential equations of first order and second order and to have qualitative applications.

CO2.   Analyzing differential equations.

CO3.   Understanding basic mechanics such as simple harmonic motion, motion under other laws and forces.

CO4.   Evaluating mechanic such as hydrodynamics, this will be helpful in getting employment in industry.

Course Content

(Differential Equations)

UNIT I                                                                                             

• Second order linear differential equations with variable coefficients: 
• Use of a known solution to find another, normal form, method of undetermined coefficient, variation of parameters, 
• Series solutions of differential equations, 
• Power series method.

UNIT II                                                                                            

• Bessel, Legendre and Hypergeometric functions and their properties, 
• recurrence and generating relations.

UNIT III                                                                                            

• Origin of first order partial differential equations. 
• Partial differential equations of the first order and degree one, 
• Lagrange's solution, 
• Partial differential equation of first order and degree greater than one. 
• Charpit's method of solution, 
• Surfaces Orthogonal to the given system of surfaces.

UNIT IV                                                                                            

• Origin of second order PDE, Solution of partial differential equations of the second and higher order with constant coefficients,
• Classification of linear partial differential equations of second order, Solution of second order partial differential equations with variable coefficients, 
• Monge's method of solution.

Part B

(Mechanics)

UNIT V                                                                                            

• Frame of reference, work energy principle, 
• Forces in three dimensions, 
• Poinsot's central axis, Wrenches, 
• Null lines and planes.

UNIT VI                                                                                           

• Virtual work, Stable and Unstable equilibrium, 
• Catenary, Catenary of uniform strength.

UNIT VII                                                                                         

• Velocities and accelerations along radial and transverse directions, and along tangential and normal directions, 
• Simple Harmonic motion, Motion under other law of forces. 
• Elastic strings, Motion in resisting medium, Constrained motion, Motion on smooth and rough plane curves.

UNIT VIII                                                                                         

• Motion of particles of varying mass, Rocket motion, 
• Central orbit, Kepler's laws of motion, Motion of particle in three dimensions, 
• Rotating frame of reference, Rotating Earth, 
• Acceleration in terms of different coordinates systems.

Suggested Readings

(Part-A Differential Equations):

1. G.F. Simmons, Differential Equations with Application and Historical Notes, Tata–McGraw Hill
2. B. Rai, D.P. Choudhary& H. J. Freedman, A Course of Ordinary Differential Equations, Narosa
3. Ian N. Snedden, Elements of Partial Differential Equations, Dover Publication
4. L.E. Elsgolts, Differential Equation and Calculus of variations, University Press of the Pacific.
5. Suggested digital plate form: NPTEL/SWAYAM/MOOCs
6. Course Books published in Hindi may be prescribed by the Universities.

 (Part-B Mechanics):

1. R.C. Hibbeler, Engineering Mechanics-Statics, Prentics Hall Publishers
2. R.C. Hibbeler, Engineering Mechanics-Dynamics, Prentics Hall Publishers
3. A. Nelson, Engineering Mechanics Statics and Dynamics, Tata McGraw Hill
4. J.L. Synge & B.A. Griffith, Principles of Mechanics, Tata McGraw Hill
5. Suggested digital plate form : NPTEL/SWAYAM/MOOCs