Solution To Homogenous And Non-Homogenous Linear Partial Differential Equations Of
Second Order By Complimentary Function And Particular Integral Method
Second-Order Linear Equations And Their Classification
Initial And Boundary Conditions
D'Alembert's Solution Of The Wave Equation
Duhamel's Principle For One Dimensional Wave Equation
Heat Diffusion And Vibration Problems
Separation Of Variables Method To Simple Problems In Cartesian Coordinates
The Laplacian In Plane, Cylindrical And Spherical Polar Coordinates
Solutions With Bessel Functions And Legendre Functions
One Dimensional Diffusion Equation And Its Solution By Separation Of Variables
Unit 2: Probability Theory
Probability Spaces
Conditional Probability
Independence
Discrete Random Variables
Independent Random Variables
The Multinomial Distribution
Poisson Approximation To The Binomial Distribution
Infinite Sequences Of Bernoulli Trials
Sums Of Independent Random Variables
Expectation Of Discrete Random Variables
Moments
Variance Of A Sum
Correlation Coefficient
Chebyshev's Inequality
Continuous Random Variables And Their Properties
Distribution Functions And Densities
Normal, Exponential And Gamma Densities
Bivariate Distributions And Their Properties
Distribution Of Sums And Quotients
Conditional Densities
Bayes' Rule
Unit 3: Basic Statistics & Distributions
Measures Of Central Tendency: Moments, Skewness And Kurtosis
Probability Distributions: Binomial, Poisson And Normal - Evaluation Of Statistical
Parameters For These Three Distributions
Correlation And Regression - Rank Correlation
Curve Fitting By The Method Of Least Squares - Fitting Of Straight Lines, Second
Degree Parabolas And More General Curves
Test Of Significance: Large Sample Test For Single Proportion, Difference Of
Proportions
Tests For Single Mean, Difference Of Means, And Difference Of Standard Deviations
Test For Ratio Of Variances - Chi-Square Test For Goodness Of Fit And Independence
Of Attributes