DIFFERENTIAL EQUATIONS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS

Here is the Modified 2016 KTU Syllabus for B-TECH KTU STUDENTS. 

KTU First year B.tech Syllabus for DIFFERENTIAL EQUATIONS.


DIFFERENTIAL EQUATIONS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS

DIFFERENTIAL EQUATIONS


Syllabus


First order ordinary differential equations, second order ordinary differential equations, higher order linear differential equations, Fourier series, partial differential equations, applications of partial differential equations.


Text Book:- 


  • Erwin Kreyszig: Advanced Engineering Mathematics, Wiley

  • A C Srivastava, P K Srivasthava, Engineering Mathematics Vol 2. Phi Learning Private Ltd


Module 1 Contents


FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS (Book 1. Sections: 1.1, 1.3, 1.4, 1.5, 1.6) Introduction –Basic Concepts, Modelling. Separable ODEs, Modelling- Exact ODEs, Integrating Factors-Linear ODEs.

Bernoulli Equation, Population Dynamics-Orthogonal Trajectories. (Theorems need not be proved. Sketching, plotting and interpretation of solutions of differential equations using suitable software) 


Module 2 Contents


SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (Book 1. Sections: 2.1, 2.2, 2.4, 2.7, 2.8, 2.10) Homogeneous Linear ODEs of Second Order -- Homogeneous Linear ODEs with Constant Coefficients-Modelling of free oscillations of a Mass Spring system –Non-Homogeneous ODEs-Modelling.

Forced Oscillations, Resonance – Solution by Variation of Parameters. (Theorems need not be proved. Sketching, plotting and interpretation of solutions of differential equations using suitable software)


Module 3 Contents


HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS (Book 1. Section: 3.1, 3.2, 3,2) Homogeneous linear ODEs- Initial value problem-Existence.

Uniqueness (without proof)- Homogeneous linear ODEs with constant coefficients- Non-Homogeneous linear ODEs-Method of variation of Parameters- Bending of elastic beam under a load. (Theorems need not be proved) .

   

Module 4 Contents


FOURIER SERIES (Book 2. Section: 4.1, 4.2, 4.3, 4.4) Periodic Functions-Orthogonality of Sin and Cosine functions- Euler’s formula-Fourier series for even and odd functions.

Half range expansions- half range Fourier cosine series - Half range Fourier sine series. (Use of soft ware’s to understand the convergence of Fourier series, sketching of partial sums)


Module 5 Contents 


PARTIAL DIFFERENTIAL EQUATION (Book 2. Section: 5.1.1, 5.1.2, 5.1.3, 5.1.4, 5.1.5, 5.1.9, 5.1.10, 5.2.6, 5.2.7, 5.2.8, 5.2.9, 5.2.10) Formation of PDEs-solutions of a first order PDE.

General integral from complete solution-Method for solving first order PDE-Lagrange’s Method-Linear PDE with Constant Coefficients-Solution of Linear Homogeneous PDE with Constant Coefficient.  

  
Module 6 Contents 


APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS (Book 2. Section: 6.1, 6.2, 6.3, 6.4, 6.7, 6. 8, 6. 9, 6.9.1, 6.9.2) Method of Separation of Variables- Wave equation-Vibrations of a Stretched sting.

Solution of one dimensional equation-The equation of Heat conduction – One dimensional Heat equation- Solution of one dimensional Heat equation –A long insulated rod with ends at zero temperatures- A long insulated rod with ends at non-zero temperatures.

DIFFERENTIAL EQUATIONS 1 YEAR SYLLABUS 2016 FOR KTU B-TECH S1 S2 STUDENTS

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