
Lecture Notes
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2.1 SEQUENCES  DEFINITIONS AND EXAMPLES,
2.2 SERIES  TYPES AND CONVERGENCE,
2.3 – SERIES OF POSITIVE TERMS,
2.4 TEST OF CONVERGENCE,
2. 5 D’ALEMBERT’S RATIO TEST,
2. 6 D’ALEMBERT’S RATIO TEST 
Lecture Notes
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4.2 DIFFERENTIATION OF IMPLICIT FUNCTIONS, JACOBIAN AND PROPERTIES,
4.1 PARTIAL DERIVATIVE AND TOTAL DERIVATIVES ,
4.3 PROBLEMS ON JACOBIAN ,
4.4 TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES.,
4.5 TAYLOR SERIES FOR FUNCTIONS OF TWO VARIABLES.,
4.6 MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES,
4.7 MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES 
Lecture Notes
Dear Students the Lecture Notes has been uploaded for the following topics:
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 
Question Bank
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IAE II QUESTION BANK 
Lecture Notes
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3.1 – CURVATURE AND RADIUS OF CURVATURE,
3.2 – RADIUS OF CURVATURE,
3.3 – CENTRE OF CURVATURE,
3.4 – CIRCLE OF CURVATURE,
3.5 – EVOLUTES,
3.6 – EVOLUTES,
3.7 – PROPERTIES OF EVOLUTES,
3.8 – ENVELOPES,
3.9 – ENVELOPES 
Question Bank
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IAE Question Bank 
Lecture Notes
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4.8 LAGRANGES METHOD,
4.9 LAGRANGES METHOD 
Lecture Notes
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2.5 – INTEGRAL TEST,
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 
Lecture Notes
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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 
Lecture Notes
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5.1 Higher order linear differential equations with constant coefficients (RHS = e^ax, sinax (or) cosax),
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],
5.7 Legendres linear equations,
5.1 HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS (RHS = e^ax, sinax (or) cosax),
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]