## MySkill Academy |

12thMat-2 Course Topics

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 | |

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) | |

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 | |

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 |

Unit 11 : Theory of Probability | distribution functions, probability, general distribution, mathematical expectation, Mean and Variance, binomial distribution |

12thMat-2 Course Plan