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Course Structure
The Curriculum Section of this Course covers the following Content :
Lecture 1: Number System
Lecture 2: Simplification
Lecture 3: HCF and LCM
Lecture 4: Averages
Lecture 1: Quadratic Equations
Lecture 2: Sequence and Series
Lecture 3: Surds and Indices
Lecture 4: Logarithms and Their Properties
Lecture 1: Percentage
Lecture 2: Profit and Loss
Lecture 3: Simple Interest
Lecture 4: Compound Interest
Lecture 1: Ratio, Proportion and Variation
Lecture 2: Partnership
Lecture 3: Mixture / Alligation
Lecture 1: Time, Speed and Distance
Lecture 2: Time and Work
Lecture 3: Probability
Lecture 4: Permutations and Combinations
Lecture 1: Geometry
Lecture 2: Mensuration
Lecture 3: Trigonometry
Lecture 1: Series Completion
Lecture 2: Non - Verbal Series
Lecture 3: Coding - Decoding
Lecture 4: Distance and Directions
Lecture 1: Calendar
Lecture 2: Clock
Lecture 3: Ranking & Arrrangements
Lecture 4: Puzzles
Lecture : Data Interpretation - Mean, Median, Mode and Measures of Dispersion
Lecture 1: Tabulation
Lecture 2: Bar Graphs
Lecture 3: Pie - Charts
Lecture 4: Line - Graphs
Lecture 1: Set Theory and Real Number System
Lecture 2: Relations and Functions
Lecture 3: Sequence and Series
Lecture 1: Function
Lecture 2: Extrema Subject to Two Constraints
Lecture 3: Constrained Extrema of Quadratic Forms
Lecture 4: Extrema Subject to One Constraint
Lecture 5: Method of Lagrange Multipliers
Lecture 6: Maxima and Minima of Two Variables
Lecture 7: Differentiability of Two Variables
Lecture 8: Partial Derivatives
Lecture 9: Continuity of a Function of Two Variables
Lecture 10: Limit of a Function of Two Variables
Lecture 11: Functions of Two Variables
Lecture 12: Maxima and Minima of One Variable
Lecture 13: Taylors Theorem
Lecture 14: Mean Value Theorem
Lecture 15: Rolles Theorem
Lecture 16: Derivability of a Function of One Variable
Lecture 17: Continuous Functions of One Variable
Lecture 18: Limit of a Function of One Variable
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 Function
Lecture 3: Power Series
Lecture 4: Polynomials
Lecture 5: Geometry of Complex Numbers
Lecture 6: De Moivres Theorem
Lecture 7: Monovalent Function
Lecture 8: Multivalued Function
Lecture 9: Chardal Distance
Lecture 10: Stereographic Projection
Lecture 11: Complex Plane
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: Eulers Phi Function
Lecture 3: Chinese Remainder Theorem
Lecture 4: Congruences
Lecture 5: The Greatest Common Divisor
Lecture 6: Divisibility
Lecture 7: Fundamental Theorem of Arithmetic
Lecture 8: Derangements
Lecture 9: The Inclusion-Exclusion Principle
Lecture 10: The Pigeonhole Principle
Lecture 11: Combinations
Lecture 12: Permutations
Lecture 13: Primitive Roots
Lecture 1: Binary Operations
Lecture 2: Sylow Packages
Lecture 3: Maximal Normal Subgroup
Lecture 4: Quotient Group
Lecture 5: Conjugate Subgroup
Lecture 6: Simple Group
Lecture 7: Normal Subgroup
Lecture 8: Dihedral Group Dn
Lecture 9: Cayleys Theorem
Lecture 10: Conjugate Elements
Lecture 11: Homomorphism
Lecture 12: Permutation Group
Lecture 13: Product of Subgroups
Lecture 14: Cosets
Lecture 15: Cyclic Group
Lecture 16: Subgroup
Lecture 17: Group
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: Partial Correlation and Partial Regression
Lecture 3: The Wishart Distribution
Lecture 4: Multivariate Normal Distribution
Lecture 5: Logistic Regression
Lecture 6: Regression Analysis
Lecture 7: Mixed Effect Model
Lecture 8: Analysis of Covariance (ANOCOVA)
Lecture 9: Fixed and Random Effects Models
Lecture 10: Analysis of Variance
Lecture 11: Testing of Hypothesis
Lecture 12: Confidence Intervals
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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