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(Part 2 (Integrals (inverse of differentiation, methods of integrations|,…
Part 2
Integrals
inverse of differentiation
methods of integrations|
integrals of someparticular functions
integration by partial fractions
integration by parts
definite integral
fundamental theoremof calculas
evaluation of definite integrals
properties of definite integrals
3 d
Direction cosines
equation of a line in space
angle between two lines
|shortest distance between 2 lines
plane
coplanarity
angle between2 planes
distance of a point from a plane
angle between a line and plane
probablity
Conditional probablity
multiplication theorem on probablity
independent events
bayes theorem
random variables and probab distribution
bernoulli trial andbinomial distribution
vector algebra
basic concepts
type of vectors
addition of vectors
multiplication of vector by scalar
product of 2 vectors
differential equations
basic concepts
general and particular soln of a differential
formation of diff eqn whose diff eqn is given
mehtods of solving first order ,first degree diff equations
App of integrals
area under simple curves
are between 2 curves
linear programming
LPP and mathematical formulation
different types of lpp
Part 1
Matrices
matrix
types of matrices
operations on matrices
transpose of matrix
symetric and skew symmertric
elementary operation}
invertible matrices
continuity and differentiability
Continuity
Differentiability
exponntial and logarithmic
logarithmic differentiation
derivatives of functions in parametric
second order derivatives
mean value theorem
determinants
Determnant
properties of determinants
area of a triangle
minor and cofactors
adjoint and inverse of a matrix
application fo determinant and matrices
app of derivatives
Rate of change of quantities
increasingand decreasing functions
tangents and normals
approximations
maxima and minima
Relations and functions
types of relations
types of functions
composition of function and invertible functions
binary operations
Inverse trigno funtions
basics
properties of inverse trigno functions
Class 11
Part 1
Sets
Representation
Empty set
Finite and infinitw
equal sets
Subsets
power sets
universal sets
universal sets
venn diagrams
operationson sets
complement on set
Practical problems on sets
relations and functions
cartesian products of sets
relations
functions
Trigno functions
Angles
trigno functions
trigno f(x) of sum and difference of 2 angles
trigno equations
princple of mathematical induction
Principle
Motivation
Complex nos
Complex nos
algebra
modulas and the conjugate
argand plane and polar representations
quad equatins
linear inequalities
Inequalities
algebraic solutions in one variable
graphical solution in 2 variable
solutin of system of linear inequality in 2 variavles
permutations and combinations
Fundamental principle of countig
permutationns
combinations
binomial theorem
Intro
binomial theorem for + integral indices
general and middle terms
Part 2
Sequence and series
sequences
series
ap
gp
relation between am and gm
sum to n termsof special sries
Straight line
Slope of line
various forms
general eqn of line
distance of a poitn from a line
conic sections
sections of a cone
circle
parabola
ellipse
hyperbola
intro to 3d geometry
Cordinate axes and cordiante planes
cordinates of a point in space
distance between two points
Section formula
Limits and derivatives
Idea of derivatives
limts
limits of trigno fnx
derivatives
Mathematical reasoning
statements
new statements from old
special words
implications
validating statements
statistics
Measures of dispersion
range
mean deviation
variance and standarddeviation
analysis of freq dist
Probablity
Random experiment
event
axiomatic approach to probablty