Engineering Maths Class.


Unit-1


  • Differential Calculus Representation of functions
  • Limit of a function
  • Continuity
  • Derivatives
  • Differentiation rules
  • Maxima and Minima of functions of one variable.

Unit-II

  • Functions of Several Variables.
  • Partial Differentiation .
  • Homogeneous functions and Euler’s Theorem .
  • Total derivative .
  • Change of Variables .
  • Jacobians.
  • Partial differentiation of implicit functions.
  • Taylor’s series for functions of two variables .
  • Maxima and minima of functions of two variables .
  • Lagrange’s method of undetermined multipliers.

Unit-III Integral Calculus :-

  • Definite and Indefinite Integrals
  • Substitution rule
  • Techniques of Integration
  • Integration by parts.
  • Trigonometric Integrals
  • Trigonometric substitutions.
  • Integration of rational functions by partial fraction.
  • Integration of irrational functions.
  • Improper integrals.

Unit IV Multiple Integrals.

  • Double integrals
  • Change of order of integration
  • Double integrals in polar coordinates.
  • Area enclosed by plane curves .
  • Triple integrals .
  • Volume of solids
  • Change of variables in double and triple integrals.

Unit V Differential Equations

  • Higher order linear differential equations with constant coefficients
  • Method of variation of parameters.
  • Homogenous equation of Euler’s and Legendre’s type.
  • System of simultaneous linear differential equations with constant coefficients.
  • Method of undetermined coefficients.



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