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Course Structure
The Curriculum Section of this Course covers the following Content :
Lecture 1: Introduction
Lecture 2: Sequence
Lecture 3: Convergent and Divergent Sequences
Lecture 4: Bounded and Unbounded Sequence
Lecture 5: Monotonic Sequence
Lecture 6: Infinite Series
Lecture 7: Upper and Lower limits
Lecture 8: Convergence Criteria for Sequences of Real Numbers
Lecture 9: Subsequence
Lecture 10: Cauchy Sequence
Lecture 11: Absolute and Conditional Convergence
Lecture 12: Tests of Convergence of Series
Lecture 13: Convergence of the Infinite Integral
Lecture 14: Alternating Series
Lecture 1: Introduction
Lecture 2: Limit of a Function of One Variable
Lecture 3: Continuous Functions of One Variable
Lecture 4: Derivability of a Function of One Variable
Lecture 5: Functions of Two Variables
Lecture 6: Limit of a Function of Two Variables
Lecture 7: Continuous Functions of Two Variables
Lecture 8: Derivability of a Function of Two Variables
Lecture 1: Rolle Theorem : Statement
Lecture 2: Mean Value Theorem
Lecture 3: Taylor Theorem
Lecture 4: Maxima and Minima of One Variable
Lecture 5: Maxima and Minima of Functions of Two Variables
Lecture 6: Indeterminate Forms
Lecture 1: Antiderivatives - Differentiation in Reverse
Lecture 2: Definite Integrals and Their Properties
Lecture 3: Differentiation Under the Integral Sign
Lecture 4: Fundamental Theorem of Calculus
Lecture 5: Arc Length
Lecture 6: Double Integral
Lecture 7: Change of Order of Integration
Lecture 8: Triple Integrals
Lecture 9: Surface Area
Lecture 10: Evaluation of Volumes
Lecture 1: Matrices
Lecture 2: Rank of Matrix
Lecture 3: Inverse of a Matrix
Lecture 4: Determinants
Lecture 5: System of Linear Equations
Lecture 6: Consistent and In-Consistent Non-Homogeneous Linear Equations
Lecture 7: Eigen Values and Eigen Vectors
Lecture 8: Linear Transformation
Lecture 1: Introduction
Lecture 2: Differential Equations
Lecture 3: Cauchy’s Problem
Lecture 4: Exact Equation and Its Solution by Insepection
Lecture 5: Integrating Factors
Lecture 6: Linear Equation
Lecture 7: Equation Reducible to Linear form or Bernoulli’s Equation
Lecture 8: Orthogonal and Oblique Trajectories
Lecture 9: Homogeneous Differential Equations
Lecture 10: Cauchy-Euler Equation
Lecture 11: Linear Equations of Second Order with Variable Coefficients
Lecture 12: Method of Variation of Parameters
Lecture 1: Introduction
Lecture 2: Classical Approach to Probability
Lecture 3: Axiomatic Approach to Probability
Lecture 4: Addition Theorems on Probability
Lecture 5: Conditional Probability
Lecture 6: Multiplication Theorems on Probability
Lecture 7: Independent Events
Lecture 8: The Law of Total Probability
Lecture 9: Baye's Rule
Lecture 1: Random Variable
Lecture 2: Distribution Function
Lecture 3: Discrete Random Variable
Lecture 4: Continuous Random Variable
Lecture 5: The Distribution of a Function of a Random Variable
Lecture 6: Cumulative Distribution Functions
Lecture 1: Mathematical Expectation
Lecture 2: Covariance, Variance of Sums, and Correlations
Lecture 3: Conditional Expectation
Lecture 4: The variance and Standard Deviation
Lecture 5: Moments
Lecture 6: Moment Generating Functions
Lecture 7: Characteristic Functions
Lecture 8: Chebyshev’s Inequality
Lecture 1: The Bernoulli and Binomial Random Variables
Lecture 2: The Poisson Random Variable
Lecture 3: The Negative Binomial Random Variable
Lecture 4: The Hypergeometric Random Variable
Lecture 5: The Zeta (or Zipf) Distribution
Lecture 6: Expectation and Variance of Continuous Random Variables
Lecture 7: The Uniform Random Variable
Lecture 8: Normal Random Variables
Lecture 9: Exponential Random Variables
Lecture 10: The Gamma Distribution
Lecture 11: The Weibull Distribution
Lecture 12: The Cauchy Distribution
Lecture 13: The Beta Distribution
Lecture 14: The Normal Approximation to The Binomial Distribution
Lecture 15: The DeMoivre-Laplace Limit Theorem
Lecture 1: Joint Probability Law
Lecture 2: Joint Probability Mass Function and Marginal
Lecture 3: Joint Probability Distribution Function
Lecture 4: Discrete Distribution Functions
Lecture 5: Marginal Distribution Function
Lecture 6: Joint and Marginal Density Functions
Lecture 7: Conditional Distributions
Lecture 8: Independent Random Variables
Lecture 9: Regression
Lecture 10: Pearson Product-Moment Correlation Coefficient
Lecture 11: Pearson’s Correlation and Least Squares Regression Analysis
Lecture 1: Exact Sampling Distributions (Chi-square Distribution)
Lecture 2: M.G.F. of Chi-square Distribution
Lecture 3: Cumulant Generating Function of Chi-square Distribution
Lecture 4: Limiting Form of Chi-square Distribution for Large Degrees of Freedom
Lecture 5: Chi-square Probability Curve
Lecture 6: Chi-square Test of Goodness of Fit
Lecture 7: Non-central Chi-square Distribution
Lecture 8: Student's 't' Distrbution
Lecture 9: Moment Generating Function of t-Distribution
Lecture 10: Applications of t-Distribution
Lecture 11: Non-central t-Distribution
Lecture 12: F-statistic
Lecture 13: Mode and Points of Inflexion of F-Distribution
Lecture 14: Applications of F-Distribution
Lecture 15: Relation between t and F-Distributions
Lecture 16: Relation between F and Chi-square
Lecture 17: Non-Central F-Distribution
Lecture 1: Introduction
Lecture 2: Chebyshev’s Inequality and The Weak Law of Large Numbers
Lecture 3: The Central Limit Theorem
Lecture 4: The Strong Law of Large Numbers
Lecture 1: Introduction
Lecture 2: Consistency
Lecture 3: Unbiasedness
Lecture 4: Efficient Estimators
Lecture 5: Minimum Variance Unbiased (M.V.U.) Estimators
Lecture 6: Sufficiency
Lecture 7: Completeness
Lecture 8: Factorization Theorem
Lecture 9: Cramer-Rao Inequality
Lecture 10: Rao-Blackwellisaton
Lecture 11: Lehmann-Scheffe Theorem
Lecture 12: Method of Maximum Likelihood Estimation
Lecture 13: Method of Moments
Lecture 14: Confidence Interval and Confidence Limits
Lecture 15: Confidence Intervals for One Parameter Exponential Distributions
Lecture 1: Introduction
Lecture 2: Basic Concepts of Hypothesis Testing
Lecture 3: Test of Hypothesis about Population Mean
Lecture 4: Steps in Solving Testing of Hypothesis Problem
Lecture 5: Most Powerful Test (MP Test)
Lecture 6: Uniformly Most Powerful Test (UMP Test)
Lecture 7: Neyman-Pearson Lemma for Testing Simple and Composite Hypotheses
Lecture 8: Likelihood Ratio Tests
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Amit Kumar
Dnyaneshwar Jadhav
Chetan