JAM ACHIEVER - Mathematics (2017)

Joint Admission Test for M.Sc.(IIT JAM)

Complete Comprehensive Course Material

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Course Structure

The Curriculum Section of  this Course covers the following Content :

  • 15 Units of Theory
  • 15 Topic wise Unit Solved Papers (USPs)
  • 5 Volume Solved Papers (VSPs)
  • 8 Full Length Model Solved Papers (MSPs)
  • 3 Previous Year Solved Papers (2014, 2015, 2016) (PSPs)

Module: JAM THEORETICAL COURSE - Mathematics

  • Subject: Mathematics
    • Section : Units
      • Unit 1: Sequences and Series

        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

      • Unit 2: Convergence of Sequences

        Lecture 1: Upper and Lower Limits

        Lecture 2: Convergence Criteria for Sequences of Real Numbers

        Lecture 3: Subsequence

        Lecture 4: Cauchy Sequence

        Lecture 5: Absolute and Conditional Convergence

      • Unit 3: Convergence of Series

        Lecture 1: Tests of Convergence of Series

        Lecture 2: Convergence of the Infinite Integral

        Lecture 3: Alternating Series

      • Unit 4: Functions of One Variable

        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: RolleÂ’ Theorem

        Lecture 6: Mean Value Theorem

        Lecture 7: TaylorÂ’ Theorem

        Lecture 8: Maxima and Minima of One Variable

      • Unit 5: Functions of Two Real Variables - I

        Lecture 1: Introduction

        Lecture 2: Limit of a Function of Two Variables

        Lecture 3: Continuity of a Function of Two Variables

        Lecture 4: Partial Derivatives

        Lecture 5: Differentiability of Two Variables

        Lecture 6: Maxima and Minima of Two variables

      • Unit 6: Functions of Two Real Variables - II

        Lecture 1: Method of Lagrange Multipliers

        Lecture 2: Extrema Subject to One Constraint

        Lecture 3: Constrained Extrema of Quadratic Forms

        Lecture 4: Extrema Subject to Two Constraints

        Lecture 5: EulerÂ’ Homogeneous Function Theorem

      • Unit 7: Integral Calculus

        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: Double Integrals

        Lecture 6: Change of Order of Integration

        Lecture 7: Triple Integrals

        Lecture 8: Surface Area

        Lecture 9: Evaluation of Volumes

      • Unit 8: Differential Equations - I

        Lecture 1: Differential Equations

        Lecture 2: CauchyÂ’ Problem

        Lecture 3: Exact Equation and Its Solution by Insepection

        Lecture 4: Integrating Factors

        Lecture 5: Linear Equation

        Lecture 6: Equation Reducible to Linear form or BernoulliÂ’s Equation

        Lecture 7: Orthogonal and Oblique Trajectories

      • Unit 9: Differential Equations - II

        Lecture 1: Introduction

        Lecture 2: Homogeneous Differential Equations

        Lecture 3: Cauchy-Euler Equation

        Lecture 4: Linear Equations of Second Order with Variable Coefficients

        Lecture 5: Method of Variation of Parameters

      • Unit 10: Vector Calculus

        Lecture 1: Scalar and Vector

        Lecture 2: Vector Function of a Single Scalar Variable

        Lecture 3: Gradient of a Scalar Point Function

        Lecture 4: Divergence of a Vector Point Function

        Lecture 5: Curl of a Vector Point Function

        Lecture 6: Line Integral

        Lecture 7: Surface Area and Surface Integrals

        Lecture 8: Volume Integral

        Lecture 9: GausÂ’s Divergence Theorem

        Lecture 10: StokeÂ’ Theorem

        Lecture 11: GreenÂ’ Theorem

      • Unit 11: Group Theory - I

        Lecture 1: Preliminaries

        Lecture 2: Group

        Lecture 3: Abelian Group

        Lecture 4: Non-Abelian Group

        Lecture 5: Subgroup

        Lecture 6: Cyclic Groups

        Lecture 7: Permutation

        Lecture 8: Normal Subgroup

      • Unit 12: Group Theory - II

        Lecture 1: Cosets

        Lecture 2: LagrangeÂ’ Theorem and Consequences

        Lecture 3: Morphism

        Lecture 4: Group Homomorphism

        Lecture 5: Factor Groups

      • Unit 13: Linear Algebra - I

        Lecture 1: Vector Spaces

        Lecture 2: Linear Combination

        Lecture 3: Spanning Set

        Lecture 4: Subspaces

        Lecture 5: Linear Dependence and Independence

        Lecture 6: Basis and Dimension

        Lecture 7: Linear Transformation

        Lecture 8: Vector Space Isomorphism

        Lecture 9: Kernel and Image of a Linear Mapping

        Lecture 10: Rank and Nullity of a Linear Mapping

        Lecture 11: Rank-Nullity Theorem

      • Unit 14: Linear Algebra - II

        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

      • Unit 15: Real Analysis

        Lecture 1: Some Basic Definitions

        Lecture 2: Bounded Set

        Lecture 3: Completeness of R

        Lecture 4: Limit Points

        Lecture 5: The Archimedean Property of Real Numbers

        Lecture 6: Intervals

        Lecture 7: Open and Closed Sets

        Lecture 8: Interior and Exterior of A Set

        Lecture 9: Compactness

        Lecture 10: Connectedness

        Lecture 11: Power Series

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