Answer Key for Previous year Questions # • MATRICES AND CALCULUS/...
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#offlineclass2022 # 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.
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
#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.
#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.
#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
Негізгі бет HOW TO STUDY ARREAR EXAM| VERY VERY IMPORTANT TOPICS OF MATRICES AND CALCULUSI| ENGINEERING MATHS|
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