Properties of Eigen values & Eigen Vectors in Tamil | Unit 1| MA 3151| Class-I
Matrices and Calculus MA3151 Anna University Syllabus Symmetric Matrices with Non-Repeated Eigen Values Eigen Values and Eigen Vectors Class 1 # • Eigen values & Eigen Vectors in Tamil | Un... 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 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 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 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 centers of mass, moment of inertia. jeyamarriya #engineeringmaths #matricesandcalculus #matrices&calculus #MA3151 #eigenvalues&eigenvectors
