MT-221 LINEAR ALGEBRA & ORDINARY DIFFERENTIAL EQUATIONS
CREDIT HOURS
Theory = 3
Practical = 0
COURSE LEARNING OUTCOMES (CLOs)
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COURSE CONTENT
- Linear Algebra: Linearity and linear dependence of vectors, basis, dimension of a vector space, field matrix and type of matrices (singular, non- singular, symmetric, non- symmetric, upper, lower, diagonal), Rank of a matrix using row operations and special method, echelon and reduced echelon forms of a matrix, determination of consistency of a system of linear equation using rank, matrix of linear transformations, eigen value and eigen vectors of a matrix, Diagonolization. Applications of linear algebra in relevant engineering problem.
- 1st Order Differential Equations: Basic concept: Formation of differential equations and solution of differential equations by direct integration and by separating the variables: Homogeneous equations and equations reducible to homogeneous from; Linear differential equations of the order and equations reducible to the linear form; Bernoulli's equations and orthogonal trajectories: Application in relevant Engineering.
- 2nd and Higher Orders Equations: Special types of IInd order differential equations with constant coefficients and their solutions: The operator D; Inverse operator I/D; Solution of differential by operator D methods; Special cases, Cauchy's differential equations; Simultaneous differential equations; simple application of differential equations in relevant Engineering.
- Partial Differential Equation: Basic concepts and formation of partial differential equations: Linear homogeneous partial differential equations and relations to ordinary differential equations: Solution of first order linear and special types of second and higher order differential equations; D’ Alembert's solution of the wave equation and two dimensional wave equations: Lagrange's solution; Various standard forms.
- Fourier Series: Periodic functions and expansion of periodic functions in Fourier series and Fourier coefficients: Expansion of function with arbitrary periods. Odd and even functions and their Fourier series; Half range expansions of Fourier series.
RECOMMENDED BOOKS
Text/Reference Book(s)
- Howard Anton, "Elementary Linear Algebra", 7th Edition.
- Erwin Kreyszig, "Advance Engineering Mathematics", 7th Edition.
- Robert L. Barrelli,"Differential Equation A modeling Perspective", 1998
- J. Farlaw, "Introduction to Differential Equation",1994
- G. zill, "Differential Equation"
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