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GE3252 தமிழர்மரபு - Coggle Diagram
GE3252 தமிழர்மரபு
அலகு I ம ொழிமற்றும்இலக்கியம்
Diagonalization of matrices by orthogonal transformation
Reduction of a quadratic form to canonical form by orthogonal transformation
Cayley - Hamilton theorem
Nature of quadratic forms
Properties of Eigenvalues and Eigenvectors
Applications : Stretching of an elastic membrane
Characteristic equation
ACTIVITY
Assignment
Eigenvalues and Eigenvectors of a real matrix
திராவிட
ம ொழிகள்
இந்திய ம ொழிக்
குடும்பங்கள்
ACTIVITY
Assignment
UNIT IV
INTEGRAL CALCULUS
Integration of rational functions by partial fraction
Integration of irrational functions
Trigonometric substitutions
Trigonometric integrals
Improper integrals
Techniques of Integration : Integration by parts
Applications : Hydrostatic force and pressure, moments and centres of mass
Substitution rule
ACTIVITY
Assignment
Definite and Indefinite integrals
UNIT II DIFFERENTIAL CALCULUS
Differentiation rules (sum, product, quotient, chain rules)
Implicit differentiation
Derivatives
Logarithmic differentiation
Continuity
Applications : Maxima and Minima of functions of one variable
Limit of a function
Representation of functions
ACTIVITY
QUIZ
UNIT III FUNCTIONS OF SEVERAL VARIABLES
Partial differentiation of implicit functions
Taylor’s series for functions of two variables
Jacobians
Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers
Change of variables
ACTIVITY
CASE STUDY
Total derivative
Homogeneous functions and Euler’s theorem
Partial differentiation
UNIT V MULTIPLE INTEGRALS
ACTIVITY
SEMINAR
Applications : Moments and centres of mass, moment of inertia
Change of variables in double and triple integrals
Volume of solids
Triple integrals
Area enclosed by plane curves
Double integrals in polar coordinates
Change of order of integration
Double integrals