Applied mathematics -1 Chapter wise Video Lectures

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Complex Numbers 

Pre‐requisite:
 Review of Complex Numbers‐Algebra of Complex Number, Different representations of a Complex number and other definitions, D’Moivre’s Theorem.
1.1.Powers and Roots of Exponential and Trigonometric Functions.
1.2. Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ
1.3.Circular functions of complex number

Hyperbolic functions

Hyperbolic functions. Inverse Circular and Inverse Hyperbolic functions. Separation of real and imaginary parts of all types of Functions.

 

Successive Differentiation

Successive differentiation: nth derivative of standard functions. Leibnitz’s Theorem (without proof) and problems
 OR

Partial Differentiation

Partial Differentiation: Partial derivatives of first and higher order. Total differentials, differentiation of composite and implicit functions.
4.2. Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof).Deductions from Euler’s Theorem

Jacobians

Maxima and Minima

Expansion of Functions

Taylor’s Theorem (Statement only) and Taylor’s series, Maclaurin’s series (Statement only).Expansion of 𝑒 𝑥 , sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), 𝑠𝑖𝑛−1 (𝑥),𝑐𝑜𝑠−1 (𝑥),𝑡𝑎𝑛−1 (𝑥), Binomial series.

indeterminate forms

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