FOUNDATION COURSES
ENGINEERING MATHEMATICS I
UNIT
I
MATRICES
Characteristic
equation - Eigen values and Eigen vectors of a real matrix – Statement of
Cayley- Hamilton theorem – Applications of Cayley -Hamilton theorem in finding
the inverse of a non-singular matrix and the power of a square matrix – Diagonalization of symmetric
matrices – Nature of Quadratic forms.
UNIT
II SEQUENCES AND SERIES
Sequences – Convergence of series –
Series of positive terms – Tests for
convergence (n-th term, ratio, comparison, root and integral tests) and
divergence - Leibnitz test for
alternating series –Series of positive and negative terms - Absolute and conditional convergence– Power
series – Taylor and Maclaurin series.
UNIT III DIFFERENTIAL CALCULUS OF
SEVERAL VARABLES
Limits and continuity- Partial
Derivatives – Total derivative – Differentiation of implicit functions –
inverse functions – Jacobian – Maxima
and minima of functions of two variables – Lagrange’s method of undetermined
multipliers.
UNIT
IV INTEGRAL CALCULUS OF SEVERAL
VARIABLES
Double integrals- Change of order
of integration – Double integrals in polar coordinates – Triple integrals –
Area as a double integral – Volume as a triple integral
UNIT V ORDINARY DIFFERENTIAL EQUATIONS
Higher order linear differential equations with constant coefficients –Method
of undetermined coefficients - Method of variation of parameters – Cauchy’s and
Legendre’s linear equations – Simultaneous first order linear equations with
constant coefficients- Simple Engineering Applications.
UNIT
I
MATRICES
Characteristic
equation - Eigen values and Eigen vectors of a real matrix – Statement of
Cayley- Hamilton theorem – Applications of Cayley -Hamilton theorem in finding
the inverse of a non-singular matrix and the power of a square matrix – Diagonalization of symmetric
matrices – Nature of Quadratic forms.
UNIT II SEQUENCES AND SERIES
Sequences – Convergence of series – Series of positive terms – Tests for convergence (n-th term, ratio, comparison, root and integral tests) and divergence - Leibnitz test for alternating series –Series of positive and negative terms - Absolute and conditional convergence– Power series – Taylor and Maclaurin series.
UNIT III DIFFERENTIAL CALCULUS OF
SEVERAL VARABLES
Limits and continuity- Partial
Derivatives – Total derivative – Differentiation of implicit functions –
inverse functions – Jacobian – Maxima
and minima of functions of two variables – Lagrange’s method of undetermined
multipliers.
UNIT
IV INTEGRAL CALCULUS OF SEVERAL
VARIABLES
Double integrals- Change of order
of integration – Double integrals in polar coordinates – Triple integrals –
Area as a double integral – Volume as a triple integral
UNIT V ORDINARY DIFFERENTIAL EQUATIONS
Higher order linear differential equations with constant coefficients –Method
of undetermined coefficients - Method of variation of parameters – Cauchy’s and
Legendre’s linear equations – Simultaneous first order linear equations with
constant coefficients- Simple Engineering Applications.
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