Dr. A P J Abdul Kalam Technological University / Kerala Technological university KTU First year (S1 S2) B.tech Syllabus for Differential Equations ( MA102)

Module 1 - FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

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) ( Book 1. Sections: 1.1, 1.3, 1.4, 1.5, 1.6)

Module 2 - SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS

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)(Book 1. Sections: 2.1, 2.2, 2.4, 2.7, 2.8, 2.10)

Module 3 - HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS

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) (Book 1. Section: 3.1, 3.2, 3,2)

Module 4 - FOURIER SERIES

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) (Book 2. Section: 4.1, 4.2, 4.3, 4.4)

Module 5 - PARTIAL DIFFERENTIAL EQUATION

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. (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)

Module 6 - APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

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. (Book 2. Section: 6.1, 6.2, 6.3, 6.4, 6.7, 6. 8, 6. 9, 6.9.1, 6.9.2)

Text Book:

1. Erwin Kreyszig: Advanced Engineering Mathematics, Wiley

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

References:

1. S. L. Ross. Differential Equations, Wiley

2. Mathematical Methods For Science And Engineering. Datta, Cengage Learing,

3. B. S. Grewal. Higher Engineering Mathematics, Khanna Publishers, New Delhi.

4. N. P. Bali, Manish Goyal. Engineering Mathematics, Lakshmy Publications

5. D. W. Jordan, P Smith. Mathematical Techniques, Oxford University Press

6. C. Henry Edwards, David. E. Penney. Differential Equations And Boundary Value Problems.Computing And Modeling, Pearson

Automobile Engg- K K Jain & R B Asthana, TTTI Bhopal

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