G.L

H.L

H.L

P.M

Linear Independence

1.1

1.2

1.3

1

Row Echelon form (REF) and Reduced Row Echelon form (RREF) of a Matrix

1.1  

1.2

1.3  

1

Rank of a Matrix using REF/RREF

1.1

1.2

1.3 

1

Inverse of a matrix using Gauss‑Jordan method

1.1

1.2

1.3

1

Solution of System of linear equations by elementary row operations

1.1

1.2

1.3

1

Symmetric, skew‑symmetric and orthogonal matrices

1.1

1.2

1.3

1

Eigen values and eigenvectors

1.1

1.2

1.3

1

Diagonalization of matrices

1.1

1.2

1.3

1

Inverse of a Matrix by Cayley‑Hamilton Theorem

1.1

1.2

1.3

1

H.L

H.L

P.M

​Exact differential equations

2.1

2.2 

2.3

2​

Integrating factors for non‑Exact differential equations

2.1

2.2 

2.3

2

Linear and Bernoulli’s equations

2.1

2.2

2.3

2

Equations not of first degree:

2.1

2.2

2.3

2

equations solvable for p

2.1

2.2

2.3

2

equations solvable for y

2.1

2.2

2.3

2

equations solvable for x

2.1

2.2

2.3

2

Clairaut’s type

2.1

2.2

2.3

2

G.L

H.L

H.L

P.M

Higher order linear differential equations with constant and variable coefficients

Euler‑Cauchy equations

3.1

3.2

3.3

3

Solution by variation of parameters

3.1

3.2

3.3

3

Method of undetermined coefficients

3.1

3.2

3.3

3

Classification of Ordinary and Singular points

3.1

3.2

3.3

3

Power series solutions for ordinary points

3.1

3.2

3.3

3

G.L

H.L

H.L

P.M

Differentiation

Cauchy‑Riemann equations

4.1

4.2

4.3

4

Analytic functions

4.1

4.2 

4.3

4

Harmonic functions

4.1

4.2

4.3

4

Finding harmonic conjugate

4.1

4.2

4.3

4

Analyticity of elementary functions (exponential, trigonometric, logarithm) and their properties

4.1

4.2

4.3

4