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Course Structure
The Curriculum Section of this Course covers the following Content :
Attachments 1: Introduction
Attachments 2: Sequence
Attachments 3: Convergent and Divergent Sequences
Attachments 4: Bounded and Unbounded Sequence
Attachments 5: Monotonic Sequence
Attachments 6: Infinite Series
Attachments 7: Upper and Lower limits
Attachments 8: Convergence Criteria for Sequences of Real Numbers
Attachments 9: Subsequence
Attachments 10: Cauchy Sequence
Attachments 11: Absolute and Conditional Convergence
Attachments 12: Tests of Convergence of Series
Attachments 13: Convergence of the Infinite Integral
Attachments 14: Alternating Series
Attachments 1: Introduction
Attachments 2: Limit of a Function of One Variable
Attachments 3: Continuous Functions of One Variable
Attachments 4: Derivability of a Function of One Variable
Attachments 5: Functions of Two Variables
Attachments 6: Limit of a Function of Two Variables
Attachments 7: Continuous Functions of Two Variables
Attachments 8: Derivability of a Function of Two Variables
Attachments 1: Rolle Theorem : Statement
Attachments 2: Mean Value Theorem
Attachments 3: Taylor Theorem
Attachments 4: Maxima and Minima of One Variable
Attachments 5: Maxima and Minima of Functions of Two Variables
Attachments 6: Indeterminate Forms
Attachments 1: Antiderivatives - Differentiation in Reverse
Attachments 2: Definite Integrals and Their Properties
Attachments 3: Differentiation Under the Integral Sign
Attachments 4: Fundamental Theorem of Calculus
Attachments 5: Arc Length
Attachments 6: Double Integral
Attachments 7: Change of Order of Integration
Attachments 8: Triple Integrals
Attachments 9: Surface Area
Attachments 10: Evaluation of Volumes
Attachments 1: Matrices
Attachments 2: Rank of Matrix
Attachments 3: Inverse of a Matrix
Attachments 4: Determinants
Attachments 5: System of Linear Equations
Attachments 6: Consistent and In-Consistent Non-Homogeneous Linear Equations
Attachments 7: Eigen Values and Eigen Vectors
Attachments 8: Linear Transformation
Attachments 1: Introduction
Attachments 2: Differential Equations
Attachments 3: Cauchy’s Problem
Attachments 4: Exact Equation and Its Solution by Insepection
Attachments 5: Integrating Factors
Attachments 6: Linear Equation
Attachments 7: Equation Reducible to Linear form or Bernoulli’s Equation
Attachments 8: Orthogonal and Oblique Trajectories
Attachments 9: Homogeneous Differential Equations
Attachments 10: Cauchy-Euler Equation
Attachments 11: Linear Equations of Second Order with Variable Coefficients
Attachments 12: Method of Variation of Parameters
Attachments 1: Introduction
Attachments 2: Classical Approach to Probability
Attachments 3: Axiomatic Approach to Probability
Attachments 4: Addition Theorems on Probability
Attachments 5: Conditional Probability
Attachments 6: Multiplication Theorems on Probability
Attachments 7: Independent Events
Attachments 8: The Law of Total Probability
Attachments 1: Random Variable
Attachments 2: Distribution Function
Attachments 3: Discrete Random Variable
Attachments 4: Continuous Random Variable
Attachments 5: The Distribution of a Function of a Random Variable
Attachments 6: Cumulative Distribution Functions
Attachments 1: Mathematical Expectation
Attachments 2: Covariance, Variance of Sums, and Correlations
Attachments 3: Conditional Expectation
Attachments 4: The variance and Standard Deviation
Attachments 5: Moments
Attachments 6: Moment Generating Functions
Attachments 7: Characteristic Functions
Attachments 8: Chebyshev’s Inequality
Attachments 1: The Bernoulli and Binomial Random Variables
Attachments 2: The Poisson Random Variable
Attachments 3: The Negative Binomial Random Variable
Attachments 4: The Hypergeometric Random Variable
Attachments 5: The Zeta (or Zipf) Distribution
Attachments 6: Expectation and Variance of Continuous Random Variables
Attachments 7: The Uniform Random Variable
Attachments 8: Normal Random Variables
Attachments 9: Exponential Random Variables
Attachments 10: The Gamma Distribution
Attachments 11: The Weibull Distribution
Attachments 12: The Cauchy Distribution
Attachments 13: The Beta Distribution
Attachments 14: The Normal Approximation to The Binomial Distribution
Attachments 15: The DeMoivre-Laplace Limit Theorem
Attachments 1: Joint Probability Law
Attachments 2: Joint Probability Mass Function and Marginal
Attachments 3: Joint Probability Distribution Function
Attachments 4: Discrete Distribution Functions
Attachments 5: Marginal Distribution Function
Attachments 6: Joint and Marginal Density Functions
Attachments 7: Conditional Distributions
Attachments 8: Independent Random Variables
Attachments 9: Regression
Attachments 10: Pearson Product-Moment Correlation Coefficient
Attachments 11: Pearson’s Correlation and Least Squares Regression Analysis
Attachments 1: Exact Sampling Distributions (Chi-square Distribution)
Attachments 2: M.G.F. of Chi-square Distribution
Attachments 3: Cumulant Generating Function of Chi-square Distribution
Attachments 4: Limiting Form of Chi-square Distribution for Large Degrees of Freedom
Attachments 5: Chi-square Probability Curve
Attachments 6: Chi-square Test of Goodness of Fit
Attachments 7: Non-central Chi-square Distribution
Attachments 8: Moment Generating Function of t-Distribution
Attachments 9: Applications of t-Distribution
Attachments 10: Non-central t-Distribution
Attachments 11: F-statistic
Attachments 12: Mode and Points of Inflexion of F-Distribution
Attachments 13: Applications of F-Distribution
Attachments 14: Relation between t and F-Distributions
Attachments 15: Relation between F and Chi-square
Attachments 16: Non-Central F-Distribution
Attachments 1: Introduction
Attachments 2: Chebyshev’s Inequality and The Weak Law of Large Numbers
Attachments 3: The Central Limit Theorem
Attachments 4: The Strong Law of Large Numbers
Attachments 1: Introduction
Attachments 2: Consistency
Attachments 3: Unbiasedness
Attachments 4: Efficient Estimators
Attachments 5: Minimum Variance Unbiased (M.V.U.) Estimators
Attachments 6: Sufficiency
Attachments 7: Completeness
Attachments 8: Factorization Theorem
Attachments 9: Cramer-Rao Inequality
Attachments 10: Rao-Blackwellisaton
Attachments 11: Lehmann-Scheffe Theorem
Attachments 12: Method of Maximum Likelihood Estimation
Attachments 13: Method of Moments
Attachments 14: Confidence Interval and Confidence Limits
Attachments 15: Confidence Intervals for One Parameter Exponential Distributions
Attachments 1: Introduction
Attachments 2: Basic Concepts of Hypothesis Testing
Attachments 3: Test of Hypothesis about Population Mean
Attachments 4: Steps in Solving Testing of Hypothesis Problem
Attachments 5: Most Powerful Test (MP Test)
Attachments 6: Uniformly Most Powerful Test (UMP Test)
Attachments 7: Neyman-Pearson Lemma for Testing Simple and Composite Hypotheses
Attachments 8: Likelihood Ratio Tests
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