JAM ACHIEVER COURSE Mathematics (2021)

Eduncle
IIT JAM
1

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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)
  • 10 Full Length Model Solved Papers (MSPs)
  • 5 Previous Year Solved Papers (2016, 2017, 2018, 2019, 2020) (PSPs)

Module: JAM THEORETICAL COURSE - Mathematics (MA)

  • Subject: Mathematics (MA)
    • Section 1: SEQUENCES AND SERIES
    • Section 2: Unit - 1 (Sequences of Real Numbers)

        Attachments 1: Introduction

        Attachments 2: Real Sequence

        Attachments 3: Range of a Sequence

        Attachments 4: Bounded and Monotone Sequences

        Attachments 5: Limit point of a sequence

        Attachments 6: Bolzano-Weierstrass Theorem

        Attachments 7: Limit of a sequence

        Attachments 8: Limit superior and limit inferior of Sequence

        Attachments 9: Convergent and Divergent Sequence

        Attachments 10: Algebra of Convergent Sequences

        Attachments 11: Subsequence

        Attachments 12: Cauchy Sequence

    • Section 3: Unit - 2 (Series of Real Numbers)

        Attachments 1: introduction (Series of real numbers)

        Attachments 2: Tests of Convergence of Series

        Attachments 3: Cauchys condensation test

        Attachments 4: Alternating Series

        Attachments 5: Absolute and conditional convergence

        Attachments 6: Convergence of the Infinite Integral

    • Section 4: Unit - 3 (Ponit Set Topology)

        Attachments 1: Some Basic Definitions

        Attachments 2: Bounded Set

        Attachments 3: Completeness of R

        Attachments 4: Limit Points

        Attachments 5: The Archimedean Property of Real Numbers

        Attachments 6: Intervals

        Attachments 7: Open and Closed Sets

        Attachments 8: Interior and Exterior of a set

        Attachments 9: Compactness

        Attachments 10: Connectedness

        Attachments 11: Power Series

    • Section 5: Unit - 4 (Functions of One Variable-I)

        Attachments 1: Introduction

        Attachments 2: Bounded function

        Attachments 3: Limit of a Function of one variable

        Attachments 4: Monotonic Functions

        Attachments 5: Continuous Functions of one variable

        Attachments 6: Differentiability of a Function of one variable

        Attachments 7: Intermediate value property

    • Section 6: Unit - 5 (Functions of One Variable-II)

        Attachments 1: Rolle’s Theorem

        Attachments 2: Mean Value Theorem

        Attachments 3: Taylor’s theorem

        Attachments 4: Maxima and Minima of one variable

        Attachments 5: Indeterminate Forms And L Hospitals Rule

    • Section 7: Unit - 6 (Functions of Two or Three Real Variables)

        Attachments 1: Introduction

        Attachments 2: Limit of a Function of Two Variables

        Attachments 3: Continuity of a Function of two Variables

        Attachments 4: Partial Derivatives

        Attachments 5: Differentiability of two Variables

        Attachments 6: Maxima and Minima of Functions of two variables

        Attachments 7: Function of Three Variables

        Attachments 8: Method of Lagrange Multiplier

    • Section 8: Unit - 7 (Basic Integration)

        Attachments 1: Antiderivatives - differentiation in reverse

        Attachments 2: definite integrals and their properties

    • Section 9: Unit - 8 Integral Calculus

        Attachments 1: Differentiation Under the Integral Sign

        Attachments 2: Fundamental Theorem of Calculus

        Attachments 3: Double integral

        Attachments 4: Change of order of Integration

        Attachments 5: Triple Integrals

        Attachments 6: Surface Area

        Attachments 7: Evaluation of Volumes

    • Section 10: Unit - 9 (Vector Calculus)

        Attachments 1: Scalar and vector

        Attachments 2: Vector function of a single Scalar variable

        Attachments 3: Gradient of a Scalar Point Function

        Attachments 4: Divergence of a Vector Point Function

        Attachments 5: Curl of a Vector Point Function

        Attachments 6: Line Integral

        Attachments 7: Surface Area and Surface Integrals

        Attachments 8: Volume Integral

        Attachments 9: Gauss’s Divergence Theorem

        Attachments 10: Stoke’s Theorem

        Attachments 11: Green’s Theorem

    • Section 11: Unit - 10 (Differential Equations-I)

        Attachments 1: Differential Equations

        Attachments 2: Cauchys problem

        Attachments 3: Exact equation and its solution by insepection

        Attachments 4: Integrating factors

        Attachments 5: Linear Equation

        Attachments 6: Equation reducible to linear form or Bernoullis equation

        Attachments 7: Orthogonal and Oblique Trajectories

    • Section 12: Unit - 11 (Differential Equations-II)

        Attachments 1: Introduction

        Attachments 2: Homogeneous differential equations

        Attachments 3: Cauchy-Euler Equation

        Attachments 4: Linear Equations of Second Order with Variable Coefficients

        Attachments 5: Method of Variation of Parameters

    • Section 13: Unit - 12 (Group Theory)

        Attachments 1: Preliminaries

        Attachments 2: Group

        Attachments 3: Abelian Group

        Attachments 4: Non-Abelian Group

        Attachments 5: Subgroup

        Attachments 6: Normal Subgroup

        Attachments 7: Cyclic Groups

        Attachments 8: Permutation

        Attachments 9: Dihedral Group

        Attachments 10: Cosets

        Attachments 11: Lagrange’s Theorem and Consequences

        Attachments 12: Morphism

        Attachments 13: Group Homomorphism

        Attachments 14: Factor Groups

        Attachments 15: Group Action

    • Section 14: Unit - 13 Vector Space and Linear Transformation)

        Attachments 1: Vector Spaces

        Attachments 2: Linear Combination

        Attachments 3: Spanning Set

        Attachments 4: Subspaces

        Attachments 5: Linear Dependence and Independence

        Attachments 6: Basis and Dimension

        Attachments 7: Linear Transformation

        Attachments 8: Vector Space Isomorphism

        Attachments 9: Kernel and Image of a Linear Mapping

        Attachments 10: Rank and Nullity of a Linear Mapping

        Attachments 11: Rank-Nullity Theorem

    • Section 15: Unit - 14 (Matrices and Determinants)

        Attachments 1: Matrices

        Attachments 2: Rank of Matrix

        Attachments 3: Inverse of a Matrix

        Attachments 4: Determinants

    • Section 16: Unit - 15 (System of Linear Equations and Eigen Values and Eigen Vectors)

        Attachments 1: System of Linear Equations

        Attachments 2: Consistent and In-Consistent Non-Homogeneous Linear Equations

        Attachments 3: Eigen Values and Eigen Vectors

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