**ENGINEERING MATHEMATICS 1 UNIT WISE Important Questions and Answers :-**

**UNIT I : MATRICES**

- Eigenvalues and Eigenvectors
- Cayley-Hamilton Theorem
- Reduction of a quadratic form to canonical form

**UNIT II : SEQUENCES AND SERIES**

- Tests of convergence
- Integral test and D’Alembert’s ratio test
- Leibnitz’s test
- Absolute and conditional convergence

**UNIT III : APPLICATIONS OF DIFFERENTIAL CALCULUS**

- Centre and radius of curvature
- Evolutes
- Envelopes

**UNIT IV : DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES**

- 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**

- Change of variables in double integrals
- Triple integrals – Volume of Solids.
- Area enclosed by plane curves

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