Engineering Mathematics 1 syllabus
UNIT I -MATRICES
Eigenvalues and Eigen vectors of a real matrix – Characteristic equation – Properties of eigenvalues and Eigenvectors – Statement and applications of Cayley-Hamilton Theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.
UNIT II-SEQUENCES AND SERIES
Sequences: Definition and examples – Series: Types and Convergence – Series of positive terms – Tests of convergence: Comparison test, Integral test and D’Alembert’s ratio test – Alternating series – Leibnitz’s test – Series of positive and negative terms – Absolute and conditional convergence.
UNIT III-APPLICATIONS OF DIFFERENTIAL CALCULUS
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes- Envelopes – Evolute as envelope of normals.
UNIT IV-DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES
Limits and Continuity – Partial derivatives – Total derivative – Differentiation of implicit functions – Jacobian and properties – Taylor’s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange’s method of undetermined multipliers.
UNIT V-MULTIPLE INTEGRALS
Double integrals in cartesian and polar coordinates – Change of order of integration – Area enclosed by plane curves – Change of variables in double integrals – Area of a curved surface – Triple integrals- Volume of Solids.
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