Mumbai University
APPLIED MATHEMATICS II
APPLIED MATHEMATICS - II
Differential Equations:
1. Exact differential Equations and those which can be made exact by use of integrating factor. Integrating factor by inspection,
Linear equations & reducible to linear (Bernoulli equations), method of substitution to reduce the eqn. to one of the above forms.
2. Linear Diff. Eqn. of nth order with constant coefficients, complimentary function & particular integral when the function of the integral on the R.H.S. are exponential, Sin(ax + b), Cos(ax + b).Cauchys Linear equation( Homogenous eqn.). The Legendre Linear equation, Variation of parameters & method of undetermined coefficients.
3. Elementary application of above diff. Eqn. in solving engineering problems from Electrical Engg., Chemical Engg., Mechanical Engg., and Civil Engg.
Integral Calculus: Rectification of plane curves, Double and Triple integrals, Their geometrical interpretation & evaluation. Evaluation of double integrals by change of order and change to polar. Application of double and triple integrals to areas, volumes & mass.
Beta & Gamma Functions:
1. Beta & Gamma function & their properties, relation between Beta & Gamma functions.
2. Error Functions.
3. Differentiation under the integral sign.
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