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DECODE-Engineering Mathematics - I ( BATU )

Dr. H. R. Bhapkar ISBN-9789333218962
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Unit 1
Linear Algebra - Matrices : Inverse of a matrix by Gauss - Jordan method; Rank of a matrix; Normal form of a matrix Consistency of non - homogenous and homogenous system of linear equations; Eigen values and eigen vectors; Properties of eigen values and eigen vectors (without proofs); Cayley - Hamilton's theorem (without proof) and its applications. (Chapters - 1,2,3)
Unit 2
Partial Differentiation : Partial derivatives of first and higher orders; Homogenous functions - Euler's Theorem for functions containing two and three variables (with proofs); Total derivatives; Change of variables. (Chapter - 4)
Unit 3
Applications of Partial Differentiation : Jacobians - Properties; Taylor's and Maclaurin's theorems (without proofs) for functions of two variables; Maxima and minima of functions of two variables; Lagrange's method of undetermined multipliers. (Chapter - 5)
Unit 4
Reduction Formulae and Curve Tracing : Reduction formulae for , , ; Tracing of the curves given in Cartesian, parametric and polar forms. (Chapters - 6, 7)
Unit 5
Multiple Integrals : Double integration in Cartesian and polar co - ordinates; Evaluation of double integrals by changing the order of integration and changing to polar form; Triple integral; Applications of multiple integrals to find area as double integral, volume as triple integral and surface area. (Chapters - 8,9)

 

Unit 1
Linear Algebra - Matrices : Inverse of a matrix by Gauss - Jordan method; Rank of a matrix; Normal form of a matrix Consistency of non - homogenous and homogenous system of linear equations; Eigen values and eigen vectors; Properties of eigen values and eigen vectors (without proofs); Cayley - Hamilton's theorem (without proof) and its applications. (Chapters - 1,2,3)
Unit 2
Partial Differentiation : Partial derivatives of first and higher orders; Homogenous functions - Euler's Theorem for functions containing two and three variables (with proofs); Total derivatives; Change of variables. (Chapter - 4)
Unit 3
Applications of Partial Differentiation : Jacobians - Properties; Taylor's and Maclaurin's theorems (without proofs) for functions of two variables; Maxima and minima of functions of two variables; Lagrange's method of undetermined multipliers. (Chapter - 5)
Unit 4
Reduction Formulae and Curve Tracing : Reduction formulae for , , ; Tracing of the curves given in Cartesian, parametric and polar forms. (Chapters - 6, 7)
Unit 5
Multiple Integrals : Double integration in Cartesian and polar co - ordinates; Evaluation of double integrals by changing the order of integration and changing to polar form; Triple integral; Applications of multiple integrals to find area as double integral, volume as triple integral and surface area. (Chapters - 8,9)

 

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