**MA3151 Important Questions Matrix and Calculus**

MA3151 Important Questions Matrix and Calculus Regulation 2021 Anna University free download. Matrix and Calculus Important Questions MA3151 pdf download free.

**UNIT – I MATRICES **

Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal

transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane.

**UNIT – II DIFFERENTIAL CALCULUS MA3151 Important Questions Matrix and Calculus**

Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules (sum, product, quotient, chain rules) – Implicit differentiation – Logarithmic differentiation – Applications :

Maxima and Minima of functions of one variable.

**UNIT – III FUNCTIONS OF SEVERAL VARIABLES MA3151 Important Questions Matrix and Calculus**

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of

two variables – Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.

**UNIT – IV INTEGRAL CALCULUS MA3151 Important Questions Matrix and Calculus**

Definite and Indefinite integrals – Substitution rule – Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial

fraction, Integration of irrational functions – Improper integrals – Applications : Hydrostatic force and pressure, moments and centres of mass.

**UNIT – V MULTIPLE INTEGRALS **

Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals – Applications : Moments and centres of mass, moment of inertia.

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**MA3151 Syllabus Matrix and Calculus**