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Unit - 1 Differential Equations of first order and first degree

Unit–1Differential equation of first order and first degree

1.1. Linear and Bernoulli’s equation

1.2. Exact Differential equations Reducible to exact

1.3. Orthogonal trajectories

1.4. Applications Newton’s law of cooling Law of natural growth and decay

Unit - 2 Linear Differential Equations of Higher Order

UNIT–2Linear differential equations of higher order

2.3. Method of variation of parameters Legendre’s equation CauchyEuler equation.

Unit - 3 Partial Differentiation

UNIT–3Partial Differentiation

3.1. Introduction Partial differentiation

3.2. Homogeneous function

3.3. Euler’s theorem

3.4. Total derivative

3.5. Chain rule

3.6. Jacobian

3.7. Taylor’s and Maclaurin’s series expansion of function of two variables

3.8. Functional dependence independence

3.9. Applications Maxima and minima of function of two variables without constraints and Lagrange’s method with constraints

Unit - 4 Differential Calculus

UNIT–4Differential Calculus

4.1. Mean value theorem Rolle’s theorem Lagrange’s mean value theorem

4.2. Taylor’s and Maclaurin’s theorem with reminders

4.3. Indeterminate forms L’Hospital’s rule

4.4. Maxima and minima

UNIT–4

Differential Calculus

4.1. Mean value theorem Rolle’s theorem Lagrange’s mean value theorem

4.2. Taylor’s and Maclaurin’s theorem with reminders

4.3. Indeterminate forms L’Hospital’s rule

4.4. Maxima and minima

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