102. Mathematics I


FIRST TERM:

Solid Geometry: 
Cartesian, Cylindrical polar and spherical polar coordinates,
direction ratios and direction cosines,
equations of planes and straight line, shortest, distance, coordinate transformations; 
spheres, cones, cylinders elipoids, paraboloids and hyperboloids...
standard equations with illustrations tangents planes and normal

Differential Calculus: 
Review of limit, continuity and differentiality of functions of 
single variable with terminology,
properties of continuous functions; geometrical illustrations,
applications of differentiation to geometrical illustrations,
applications of differentiation to approximate computations,
successive differentiation Lobnitz rule.
Rolle's theorem cauchy's mean value theorem, 
(Lagrange mean value theorem as a special case),
Taylor and Maclaurin expansions, L' Hospital rule.
Review of maxima and minima of functions of a single variable, 
concavity and convexity of a curve,
points of inflexion, asymptotes and curvature.


SECOND TERM:

Limit, continuity and differentiability of function ,
Geometrical interpretations, differentials,
derivatives of composite and implicit function,
Derivatives of higher orders and their commutativity, 
Euler's theorem on homogeneous function, harmonic function,
Taylor expansion of functions of several variables and
maxima and minima of functions of several variables,
Langrange method of multipliers, Ordinary Differential Equation , 
First order Equation separable, exact, homogeneous, linear Bernoulli's form,
second order equations with constant coefficient,
Euler equation, methods of their solution. 
Dependence and independence of solutions. 
Wronskian systems of first order equations (simple type)

Texts / References