Complex Trigonometry: Complex Numbers:Definitions & properties. Modulus and amplitude of acomplex number, Argand’s diagram, De-Moivre’stheorem (without proof).
Vector Algebra: Scalar and vectors. Vectors additionand subtraction. Multiplication of vectors(Dot andCross products). Scalar and vector triple productssimpleproblems
Differential Calculus: Review of successive differentiation. Formulae for nth derivatives ofstandard functions- Liebnitz’s theorem(without proof). Polar curves –angle between the radius vector and the tangent pedal equation- Problems. Maclaurin’s series expansions- Illustrative examples. Partial Differentiation : Euler’s theorem for homogeneous functions of two variables. Total derivatives differentiation of composite and implicit function.Application to Jacobians
Integral Calculus: Statement of reduction formulae for sinnx, cosnx, and sinmxcosnx and evaluation ofthese with standard limits-Examples. Double and triple integrals-Simple examples.
Vector Differentiation: Differentiation of vector functions. Velocity and acceleration of a particle moving on a space curve. Scalar and vector point functions. Gradient, Divergence, Curl and Laplacian (Definitions only). Solenoidal and irrotational vector fields-Problems.
Ordinary differential equations (ODE’s): Introduction-solutions of first order and first degreedifferential equations: homogeneous, exact, linear differential equations of order one and equationsreducible to above types.