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Unit - 1 Differentiation

1.1 Successive Differentiation 1.2 Leibnitz Theorem

1.3 Continuity of a function at a point

1.4 Differentiability

Unit - 2 Limits, homogenous, Maxima Minima

2.1 LIMITS 2.2 Continuity

2.3 Differentiability of functions

2.4 Homogenous Functions

2.5 Maxima Minima

2.6 Taylor’s Theorem in several variables

2.7 Maclaurin Series

Unit - 3 Vector Calculus

3.1Vector function of scalar Quantity3.2 Vector operator Del ∇

3.3 Gradient

3.4 Divergence

3.5 Directional derivative

3.6 Solenoidal

3.7 Irrotational Field

3.8 Scalar Potential

3.9 Sums

3.10 The Line Integral

3.11 Problems on work done

3.12. Green’s Theorem

3.13 Stokes’s Theorem

3.14 Gauss divergence theorem

Unit - 4 First Order Ordinary Differential Equations

4.1 Definition Exact Equation 4.2 Equation reducible to exact

4.3 Linear equation

4.4 Bernoulli’s Equation

4.5 Clairaut’s equation

Unit - 5 Ordinary Differential Equations of Higher Orders

5.1 Linear Differential equation5.2 Method of variations of parameters

5.3 Power series solution

5.4 Legendres Differential Equation

Unit - 6 Partial differentiation

6.1 Definition 6.2 Some standard functions

6.3 Some standard rules

6.4 Sums on Standard Formula

6.5 Partial Derivatives of first order of a function of a function.

6.6 Partial Derivatives of second order of a function of a function.

6.7 Variable treated as constant

6.8 Composite function

6.9 First order Linear PDE

6.10 First order Nonlinear PDEs

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