MA3151 Matrices and Calculus Previous Year Question Papers - Anna University

UNIT 1 - Matrices

Part A

• State Cayley-Hamilton theorem
• Find sum and product of eigenvalues
• Determine nature of quadratic form
• If lambda is eigenvalue of A, find eigenvalues of A2, A-1

Part B

• Find eigenvalues and eigenvectors of a matrix
• Diagonalize a matrix using orthogonal transformation
• Reduce quadratic form to canonical form
• Use Cayley-Hamilton theorem to find A2, A-1

UNIT 2 - Differential Calculus

Part A

• Find domain and range of a function
• Test continuity/discontinuity
• State fundamental theorem of calculus
• Differentiate using chain rule / implicit differentiation

Part B

• Find maxima and minima
• Find equation of tangent and normal
• Verify Rolle's theorem / Mean Value theorem
• Solve application problems (velocity, rate of change)

UNIT 3 - Functions of Several Variables

Part A

• Find Jacobian
• State properties of Jacobians
• Expand Taylor series (first order)
• Find stationary points

Part B

• Find maxima and minima of two variables
• Solve using Lagrange multipliers
• Expand Taylor series (higher order)
• Solve total derivative / change of variables

UNIT 4 - Integral Calculus

Part A

• Evaluate basic integrals
• Test convergence of improper integrals
• Apply integration by parts

Part B

• Solve using partial fractions
• Solve using trigonometric substitution
• Find area between curves
• Solve centre of mass / moment problems

UNIT 5 - Multiple Integrals

Part A

• Evaluate double/triple integrals
• Formula for volume using triple integrals
• Define change of order of integration

Part B

• Change order of integration and evaluate
• Find area using double integrals
• Solve using polar coordinates
• Find volume using triple integrals

Most Repeated / High-Weight Questions

Eigenvalues and eigenvectors, matrix diagonalization, quadratic forms, maxima/minima problems, Jacobians, Taylor series, Rolle's and Mean Value theorems, double/triple integrals, change of order of integration, area and volume calculations.