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Course Structure
The Curriculum Section of this Course covers the following Content :
Lecture 1: Set Theory and Real Number System
Lecture 2: Relations and Functions
Lecture 3: Sequence and Series
Lecture 1: Function
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: Rolles Theorem
Lecture 6: Mean Value Theorem
Lecture 7: Taylors Theorem
Lecture 8: Maxima and Minima of One Variable
Lecture 9: Functions of Two Variables
Lecture 10: Limit of a Function of Two Variables
Lecture 11: Continuity of a Function of Two Variables
Lecture 12: Partial Derivatives
Lecture 13: Differentiability of Two Variables
Lecture 14: Maxima and Minima of Two Variables
Lecture 15: Method of Lagrange Multipliers
Lecture 16: Extrema Subject to One Constraint
Lecture 17: Constrained Extrema of Quadratic Forms
Lecture 18: Extrema Subject to Two Constraints
Lecture 19: Eulers Homogeneous Function Theorem
Lecture 1: The Riemann Integral and Improper Integral
Lecture 2: Uniform Convergence of Sequences & Series of Functions
Lecture 3: Functions of Bounded Variation, Lebesgue Measure and Metric Space
Lecture 1: Algebra of Matrices
Lecture 2: Linear Equation and Vector Space
Lecture 1: Linear Transformation
Lecture 2: Quadratic Forms and Inner Product Spaces
Lecture 1: Complex Numbers
Lecture 2: Complex Plane
Lecture 3: Stereographic Projection
Lecture 4: Chardal Distance
Lecture 5: Multivalued Function
Lecture 6: Monovalent Function
Lecture 7: De Moivres Theorem
Lecture 8: Geometry of Complex Numbers
Lecture 9: Polynomials
Lecture 10: Power Series
Lecture 11: Complex Function
Lecture 12: Analytic Functions
Lecture 1: Line Integral
Lecture 2: Important Theorems
Lecture 3: Expansion of Analytic Functions as Power Series
Lecture 4: The Zeros of an Analytic Function
Lecture 5: Residue at a Pole
Lecture 6: Cauchys Residue Theorem
Lecture 7: Mappings
Lecture 1: Combinatorics
Lecture 2: Permutations
Lecture 3: Combinations
Lecture 4: The Pigeonhole Principle
Lecture 5: The Inclusion-Exclusion Principle
Lecture 6: Derangements
Lecture 7: Fundamental Theorem of Arithmetic
Lecture 8: Divisibility
Lecture 9: The Greatest Common Divisor
Lecture 10: Congruences
Lecture 11: Chinese Remainder Theorem
Lecture 12: Eulers Phi Function
Lecture 13: Primitive Roots
Lecture 1: Binary Operations
Lecture 2: Group
Lecture 3: Subgroup
Lecture 4: Cyclic Group
Lecture 5: Cosets
Lecture 6: Product of Subgroups
Lecture 7: Permutation Group
Lecture 8: Homomorphism
Lecture 9: Conjugate Elements
Lecture 10: Cayleys Theorem
Lecture 11: Dihedral Group Dn
Lecture 12: Normal Subgroup
Lecture 13: Simple Group
Lecture 14: Conjugate Subgroup
Lecture 15: Quotient Group
Lecture 16: Maximal Normal Subgroup
Lecture 17: Sylow Packages
Lecture 18: Generalized Caylay Theorem (GCT)
Lecture 1: Ring Theory
Lecture 2: Topology
Lecture 1: Ordinary Differential Equations
Lecture 2: Differential Equations of the First Order and First Degree
Lecture 3: Singular Solution
Lecture 4: Existence and Uniqueness Theorem
Lecture 5: Homogeneous and Non-Homogeneous Linear Differential Equations
Lecture 6: Variation of Parameters
Lecture 7: Self-Adjoint Equation
Lecture 8: Greens Function
Lecture 1: Partial Differential Equations
Lecture 2: Lagranges Solution of the Linear PDE
Lecture 3: Charpits Method
Lecture 4: Cauchy Problem for First Order PDEs
Lecture 5: Classification of Second Order Partial Differential Equation
Lecture 6: Method of Separation of Variables for Laplace Heat and Wave Equation
Lecture 1: Bisectional Method
Lecture 2: False Position or Regula Falsi Method
Lecture 3: Newton-Raphson Method
Lecture 4: Solution of Simultaneous Linear Equations
Lecture 5: Interpolation
Lecture 6: Numerical Differentiation
Lecture 7: Numerical Integration
Lecture 8: Numerical Solution of Ordinary Differential Equations
Lecture 1: Calculus of Variations
Lecture 2: Linear Integral Equations
Lecture : Classical Mechanics
Lecture 1: Cumulative Frequency Distribution
Lecture 2: Measure of Dispersion
Lecture 3: Theory of Probability
Lecture 4: Markov Chain
Lecture 5: Standard Discrete Distributions
Lecture 6: Theoritical Continuous Distribution
Lecture 7: Order Statistics
Lecture 8: Sampling Distribution
Lecture 1: Methods of Estimation
Lecture 2: Confidence Interval and Confidence Limit
Lecture 3: Test of Significance
Lecture 4: Chi-Square Test of Goodness of Fit
Lecture 5: Rank Correlation
Lecture 6: Non-Parametric Test
Lecture 1: Gauss - Markov Model
Lecture 2: Confidence Intervals
Lecture 3: Testing of Hypothesis
Lecture 4: Analysis of Variance
Lecture 5: Fixed and Random Effects Models
Lecture 6: Analysis of Covariance (ANOCOVA)
Lecture 7: Mixed Effect Model
Lecture 8: Regression Analysis
Lecture 9: Logistic Regression
Lecture 10: Multivariate Normal Distribution
Lecture 11: The Wishart Distribution
Lecture 12: Partial Correlation and Partial Regression
Lecture 13: Data Reduction Techniques
Lecture 1: Theory of Sampling
Lecture 2: Ratio and Regression Methods
Lecture 3: Experimental Design
Lecture 4: Hazard Function
Lecture 5: Censoring
Lecture 1: Linear Programming Problem
Lecture 2: Simplex Method to Solve LPP
Lecture 3: Primal Dual Problem
Lecture 4: Queuing Theory
Lecture 5: Inventory Problems
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