Definitions, complex numbers as an ordered pair, real and imaginary parts, modulus and amplitude of a complex number, equality of a complex number, addition, subtraction, multiplication & division of complex numbers, polar form, Argand diagram, exponential form, expressing in the form a±ib problems
Differentiation of nth order standard functions , Leibnitz theorem (statement only) with examples, point curves, Taylor series, Maclaurin series of simple functions for single variable. Partial differentiation:Definition, Euler theorem, total differentiation , differentiation of composite and implicit functions, Jacobian’s illustrative examples and problems.
Reduction formula for functions sinnx, cosnx,sinnx cosnx. double integral , simple problems & triple integral simple problems (with standard limits) β and γ functions, properties, relation between β andγ Functions simple problems.
Solution of first order first degree differential equations – variable separable methods homogenous equation, Bernoulli’s and exact differential equations (without L F). Differential equations of second and higher orders with constant co-efficient