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Unit - 1 Calculus

UNIT– 1Calculus

1.1 Evolutes and involutes

1.2 Evaluation of definite and improper integrals

1.3 Beta and gamma functions and their properties

1.4 Applications of definite integrals to evaluate surface areas and volumes of revolutions

Unit - 2 Calculus

Unit– 2Calculus

2.2 Mean value theorem

2.3 Taylor’s and Maclaurin theorems with remainders

2.5 Maxima and minima

Unit– 2

Calculus

2.2 Mean value theorem

2.3 Taylor’s and Maclaurin theorems with remainders

2.5 Maxima and minima

Unit - 3 Sequences and series

Unit 3Sequences Series

3.1 Convergence of sequence and series

3.2 Test for convergence Power series

3.3 Taylor’s series

3.4 Series for exponential

3.5 Trigonometric and logarithm functions

3.6 Fourier series Half range and cosine series

3.7 Parseval’s theorem

Unit - 4 Multivariable Calculus (Differentiation)

Unit – 4Multivariable Calculus Differentiation

4.1 Limit

4.2 Continuity and partial derivatives

4.3 Directional derivatives

4.4 Total derivatives

4.5 Tangent plane and normal line

4.6 Maxima minima and saddle points

4.7 Method of Lagrange multipliers

4.8 Gradient Curl and divergence

Unit - 5 Matrices

UNIT – 5 Matrices

5.1 Inverse and rank of a matrix

5.2 RankNullity theorem

5.3 System of linear equations

5.4 Symmetric skewsymmetric and orthogonal matrices

5.5 Determinants

5.6 Eigen values and Eigen vectors

5.7 Diagonalization of matrices

5.8 CayleyHamiltonn theorem

5.9 Orthogonal transformation

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