UNIT 1:
1.1 INTRODUCTION TO MATRICES
1.2 EIGEN VALUES AND EIGEN VECTORS
1.3 PROBLEMS ON EIGEN VALUES AND EIGEN VECTORS
1.4 PROPERTIES ON EIGEN VALUES AND EIGEN VECTORS
1.5 CAYLEY HAMILTON THEOREM
1.6 DIAGONALIZATION OF MATRICES
1.7 REDUCTION OF QUADRATIC FORM TO CANONICAL FORM
1.8 PROBLEMS ON REDUCTION OF QUADRATIC FORM
1.9 NATURE OF QUADRATIC FORM
UNIT 2:
2.1 SEQUENCES - DEFINITIONS AND EXAMPLES
2.2 SERIES - TYPES AND CONVERGENCE
2.3 – SERIES OF POSITIVE TERMS
2.6 – D’ALEMBERT’S RATIO TEST
2.7– D’ALEMBERT’S RATIO TEST
2.8 ALTERNATING SERIES – LEIBNITZ’S TEST
2.9 ABSOLUTE AND CONDITIONAL CONVERGENCE
UNIT 3:
3.1 – CURVATURE AND RADIUS OF CURVATURE
3.2 – RADIUS OF CURVATURE
3.3 – CENTRE OF CURVATURE
3.4 – CIRCLE OF CURVATURE
3.7 – PROPERTIES OF EVOLUTES
UNIT 4:
4.2 DIFFERENTIATION OF IMPLICIT FUNCTIONS, JACOBIAN AND PROPERTIES
4.1 PARTIAL DERIVATIVE AND TOTAL DERIVATIVES
4.4 TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES.
4.5 TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES.
UNIT 5:
5.2 HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS (RHS= x^n and e^-ax φ(x))
5.3 HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [P.I= x^n sinax(or) x^n cosax]
5.1 HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS (RHS = e^ax, sinax (or) cosax)
5.4 METHOD OF VARIATION OF PARAMETERS
5.5 PROBLEMS ON METHOD OF VARIATION OF PARAMETERS
5.6 EULERS (CAUCHYS) LINEAR EQUATIONS
5.7 LEGENDRES LINEAR EQUATION
