12thMat-2 Course Topics
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Unit 8 :
Differentials and Partial Derivatives |
8.1 Differentials - definition and simple problems; Errors and Approximations - types of errors – finding approximate values,concepts of differentials; |
Partial Differentiation - First order and second order partial derivatives, Function of function rule
(two and three variables), simple problems |
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Unit 9 :
Applications of integration |
Evaluation of definite integrals - geometric
meaning of definite integrals, definite integrals (Riemann integral) as a limit of sums, fundamental theorem of integral calculus, evaluation of definite integrals by evaluating the anti-derivative, reduction
formulae, Bernoulli’s formula, Gamma integral, properties of definite integrals |
Areas and Volumes - area bounded by a curve and
coordinate axes (simple problems), area bounded by two curves, volume of a solid obtained by revolving area about an axis
(simple problems) |
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Unit 10 :
Differential equations |
10.1 Introduction to differential equations -
definition of ordinary differential equations,
order and degree of the ODE, general and
particular solutions; Formation of differential
equations - formation of differential equations
by eliminating arbitrary constants (atmost
two constants), Modeling problems of
Population growth, Bacterial growth, Newton’s
law of cooling, Radio active decay |
Solutions
of linear differential equations (First order) -
solutions of first order and first degree
differential equations: variable separable
method, homogenous differential equation,
linear differential equations,applications to
modelling: Solving the differential equations
that were formed for population growth,
bacterial colony growth, Newton’s laws of
cooling and radioactive decay |
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Unit 11 :
Theory of Probability |
11.1 Introduction to Probability - classical
definition, random experiment, sample space
and events, sure-impossible-mutually
exclusive–exhaustive events; |
Laws on probability - addition and multiplication theorems, independent and dependent events,
conditional and total probability, Bayes’
theorem, simple problems; |
Probability
distributions - introduction to random
variables, probability mass function,
probability density function, probability |
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Unit 11 :
Theory of Probability |
distribution functions, probability, general
distribution, mathematical expectation, Mean
and Variance, binomial distribution |
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