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

MySkill Academy