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FD1 :
MATHEMATICS I
1 : LIMITS
AND CONTINUITY OF A FUNCTION
2 :
DIFFERENTIATION
Definition,
Derivative by first principle, Differentiation of implicit
functions, Differentiation of trigonometric functions,
Differentiation of inverse trigonometric functions, Transformation,
Differentiation of exponential and Logarithmic Functions, Hyperbolic
functions, Derivatives of the inverse hyperbolic functions,
Differentiation with respect to a function, Differentiation of
Parametric Equations.
3 :
SUCCESSIVE DIFFERENTIATION
Calculation
of nth derivative, Leibnitz’s theorem.
4 :
GENERAL THEOREMS, EXPANSION OF FUNCTIONS.
Rolle’s
Theorem, Mean value theorem (Lagrange’s form), Increasing and
Decreasing functions, Mean value theorem (Cauchy’s form).
Expansion
of functions;
Taylor’s
expansion theorem, Maclaurin’s theorem, Taylor’s and Maclaurin’s
infinite series.
5 :
INDETERMINATE FORM
L’ Hospital’s
rule, Evaluation of % form, Evaluation of
 form,
Evaluation of  form,
Evaluation of 00, 1 ,
 0
form.
6 :
CURVATURE
Radius of
curvature, Special formula for parametric equations, Radius of
curvature at the origin.
7 : MAXIMA
AND MINIMA
Maximum and
Minimum values of a function.
8 :
ELEMENTARY INTEGRATION
Table of
elementary integrals, Simple examples.
9 :
INTEGRATION BY SUBSTITUTION
Introduction,
Change of independent variable in
 ,
Working rule to evaluate
 by
the substitution, Four important integrals, standard forms,
Integrals of tan x, cot x, sec x, cosec x.
10 :
INTEGRATION BY PARTS
 ,
 ,
Important integrals.
11 :
INTEGRATION BY PARTIAL FRACTIONS
Non-repeated
linear factor, Repeated linear factor, Linear and quadratic factors
(non-repeated) Quadratic (repeated), Integration of rational
fraction by substitution.
12 :
INTEGRATION OF IRRATIONAL ALGEBRAIC FUNCTIONS
Integration
of rational functions, integral of the type
13 :
INTEGRATION OF TRIGNOMETRIC FUNCTIONS
 ,
Reduction formula method, Integration of positive even integral,
Integrals of rational functions of sinx and cosx.
14 :
REDUCTION FORMULA
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 .
15 :
DEFINITE INTEGRALS
Definition,
Properties of definite integrals, Examples base on properties.
16 : AREAS
OF PLANE CURVES
17 :
VOLUMES AND SURFACES OF SOLIDS OF REVOLUTION
18 :
LENGTHS OF PLANE CURVES
Arc Formulae,
Arc formulae for polar equations.
19 :
SIMPSON’S RULE
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