MA3151 Matrices and Calculus Question Papers
Download MA3151 Matrices and Calculus Question Papers. In this Notes Very Useful for First Year First Semester Students.
“MA3151 Matrices and Calculus Question Papers”
“Matrices and Calculus Question Papers”
“MA3151 Question Papers”
Subject Info:
| Semester | First Semester |
| Department | Common to All Departments |
| Year | First Year |
| Regulation | R 2021 |
| Subject Code / Name | MA3151 Matrices and Calculus |
| Content | Question Papers |
Syllabus:
MA3151 Matrices and Calculus
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 centres of mass, moment of inertia.