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MATHEMATICAL PHYSICS FOR IIT JAM

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Course Description

This course covers in detail the syllabus of Mathematical Physics section of IIT JAM Physics and other M.Sc entrance exams.The topics included in this course are:

Multiple Integral
Vector Calculus
Differential Equations
Matrices
Differential Calculus
Fourier Series
Algebra of Complex Numbers

Course Content

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Beta and Gamma Function 2 Topics

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Beta and Gamma Function-1

Beta and Gamma Function-2

MULTIPLE INTEGRAL

Introduction to Double Integrals 1 Topic

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Introduction to Double Integrals

Change of Order 7 Topics Sample Lesson

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Change of Order-1

Change of Order-2

Change of Order-3

Change of Order-4

Change of Order-5

Change of Order-6

Change of Order-7

VECTOR CALCULUS

Gradient 2 Topics

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Directional Derivative

Properties of Gradient

Tangent Plane and Normal 2 Topics

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Tangent Plane and Normal

Problems on Tangent Plane and Normal

Problems on Gradient 1 Topic

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Problems on Gradient

Divergence and Curl 4 Topics

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Divergence and Curl

Problems on Divergence and Curl-1

Problems on Divergence and Curl-2

Problems on Divergence and Curl-3

Line Integral 4 Topics Sample Lesson

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Introduction to Line Integral

Problems on Line Integral-1

Problems on Line Integral-2

Problems on Line Integral-3

Greens Theorem 6 Topics

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Introduction to Green’s Theorem

Problems on Green’s Theorem-1

Problems on Green’s Theorem-2

Problems on Green’s Theorem-3

Problems on Green’s Theorem-4

Problems on Green’s Theorem-5

Surface Integral 6 Topics

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Introduction to Surface Integral

Problems on Surface Integral-1

Problems on Surface Integral-2

Problems on Surface Integral-3

Problems on Surface Integral-4

Problems on Surface Integral-5

Gauss Divergence Theorem 8 Topics

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Introduction to Gauss Divergence Theorem

Problems on Gauss Divergence Theorem-1

Problems on Gauss Divergence Theorem-2

Problems on Gauss Divergence Theorem-3

Problems on Gauss Divergence Theorem-4

Problems on Gauss Divergence Theorem-5

Problems on Gauss Divergence Theorem-6

Problems on Gauss Divergence Theorem-7

Stokes Theorem 5 Topics

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Introduction to Stoke’s Theorem

Problems on Stoke’s Theorem-1

Problems on Stoke’s Theorem-2

Problems on Stoke’s Theorem-3

Problems on Stoke’s Theorem-4

Conservative Vector Field 3 Topics

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Introduction to Conservative Vector Field

Problems on Conservative Vector Field-1

Problems on Conservative Vector Field-2

DIFFERENTIAL EQUATIONS

Introduction to Differential Equations 2 Topics

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Order and Degree

Formation of Differential Equation

Differential Equation of First order and First Degree 8 Topics

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Separation of Variables

Homogeneous Equation

Equation Reducible to Homogeneous Form

Exact Differential Equation

Integrating Factor

Integrating Factor-contd

Linear Differential Equation of first order

Equation reducible to Linear Form

Orthogonal Trajectory 2 Topics Sample Lesson

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Introduction to Orthogonal Trajectory

Problems on Orthogonal Trajectory

Differential Equation with Constant Coefficient 7 Topics

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Introduction to Differential Equation with Constant Coefficient

Complementary Function

Particular Integral

Exponential Function

Trigonometric Function

Polynomial Function

Product of Exponential and other Function

Homogeneous Linear Differential Equation 4 Topics

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Introduction to Homogeneous Linear Differential Equation

Problems on Cauchy Euler Equation-1

Problems on Euler Cauchy Equation-2

Equation reducible to cauchy Euler form

Differential Equation of Second Order 6 Topics

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Introduction to Differential Equation of Second Order

Problems on Differential Equation of Second Order

Problems on Differential equation of second order-2

Variation of Parameters

Problems on Variation of parameters

Problems on Differential Equation of Second Order

MATRICES

Introduction to Matrices 7 Topics

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Definition of Matrices

Types of Matrices

Operation on matrices

Operation on matrices-2

Transpose of matrix

Symmetric and Skew-symmetric matrices

Orthogonal matrices

Rank of Matrix 3 Topics

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Echelon Form of matrix

Problems on Rank

Linear Equations 6 Topics

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Linear Equations

Homogeneous Linear equation

Homogeneous linear equation-contd

Non-homogeneous Linear Equation

Non-homogeneous Linear Equation-contd

Finding Inverse using elementary transformation

Determinant 7 Topics

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Introduction of Determinants

Properties of Determinants

Determinant Formula

Formula for Inverse of Matrix

Kramer’s Rule

Problems on Kramer’s Rule

Problems on Determinants

Revision of Matrices 6 Topics

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Matrices- Revision

Problems on Rank

Elementary Matrix

Equivalence of matrix

Normal form of Matrix

Vector Spaces 3 Topics

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Introduction to Vector Spaces

Subspaces associated with matrix

Linear Equations – Vector Space Approach 5 Topics

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Homogeneous Linear Equations

Homogeneous Linear Equations-2

Homogeneous Linear Equations-3

Non-homogeneous Linear Equation

Non-homogeneous Linear Equation-2

Introduction to Eigenvalues and Eigenvectors 3 Topics

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Introduction to Eigenvalues and Eigenvectors

Problems on Eigenvalues and Eigenvectors-1

Problems on Eigenvalues and Eigenvectors-2

Diagonalisation of Matrices and its Applications 5 Topics Sample Lesson

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Diagonalisation

Matrix Exponential

Differential Equations

Differential Equations-contd

Fibonaaci Sequence

Properties of Eigenvalues 1 Topic

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Properties of Eigenvalues

Symmetric Matrices 3 Topics

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Symmetric Matrices

Symmetric Matrices-2

Cayley Hamilton Equation 1 Topic

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Cayley Hamilton Equation

Similar Matrices 1 Topic

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Similar Matrices

DIFFERENTIAL CALCULUS

Monotonicity 5 Topics

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Increasing and Decreasing Function

Problems on Monotonicity

Problems on Monotonicity-2

Problems on Monotonicity-3

Critical Points 3 Topics

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Critical and Stationary Points

Point of Inflexion

Problems on Point of Inflexion

Maxima and Minima 3 Topics

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Local maxima and minima

Problems on local maxima and minima

Global maxima and minima

Rolle Theorem 2 Topics

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Problems on Rolle Theorem

Lagrange Mean Value Theorem 5 Topics Sample Lesson

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Introduction to Lagrange Mean Value Theorem

Problems on Lagrange Mean Value Theorem

Problems on Lagrange Mean Value Theorem-2

Introduction to Taylor’s Theorem

Problems on Taylor’s Theorem

Function of Two Variables 7 Topics

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Introduction to Function of Two Variables

limits of Function of Two Variables

Continuity of Function of Two Variables

Partial Derivatives

Diffrentiability of Function of Two Variables

Partial Derivatives of Higher Order

Homogeneous Function

Jacobian 1 Topic

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Maxima and Minima of Function of Several Variables 2 Topics

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Maxima and Minima of Function of two Variables

Maxima and Minima of Function of Several Variables

Fourier Series 1 Topic

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