#### Topics

##### Complex Numbers Old

##### Expansion of Sinn θ,Cosn θ in Terms of Sines and Cosines Of Multiples Of θ And Expansion of Sinnθ, Cosnθ In Powers of Sinθ, Cosθ

##### Separation of Real and Imaginary Parts of All Types of Functions

##### Circular Functions of Complex Number and Hyperbolic Functions.Inverse Circular and Inverse Hyperbolic Functions. Logarithmic Functions.

##### Powers and Roots of Exponential and Trigonometric Functions

##### Matrices and Numerical Methods Old

##### Solution of System Of Linear Algebraic Equations

##### Types of Matrices and Rank of a Matrix

##### Differential Calculus Old

##### Euler’S Theorem on Homogeneous Functions with Two and Three Independent Variables (With Proof)

##### Partial Differentiation

##### Successive Differentiation

##### Application of Partial Differentiation, Expansion of Functions , Indeterminate Forms and Curve Fitting Old

##### Fitting of Curves by Least Square Method for Linear, Parabolic, And Exponential

##### Maxima and Minima of a Function of Two Independent Variables

##### Taylor’S Theorem and Taylor’S Series, Maclaurin’S Series

##### Complex Numbers

- Review of Complex Numbers‐Algebra of Complex Number
- Different Representations of a Complex Number and Other Definitions
- D’Moivre’S Theorem
- Powers and Roots of Exponential Function
- Powers and Roots of Trigonometric Functions
- Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
- Expansion of sinnθ, cosnθ in powers of sinθ, cosθ
- .Circular Functions of Complex Number
- Hyperbolic functions of complex number
- Inverse Circular Functions
- Inverse Hyperbolic Functions
- Separation of Real and Imaginary Parts of All Types of Functions

##### Logarithm of Complex Numbers , Successive Differentiation

##### Successive Differentiation

##### Logarithm of Complex Numbers

##### Matrices

- Inverse of a Matrix
- Addition of a Matrix
- Multiplication of a Matrix
- Transpose of a Matrix
- Types of Matrices
- Rank of a Matrix Using Echelon Forms
- Reduction to Normal Form
- PAQ in normal form
- System of Homogeneous and Non – Homogeneous Equations
- consistency and solutions of homogeneous and non – homogeneous equations
- Linear Dependent and Independent Vectors
- Application of Inverse of a Matrix to Coding Theory

##### Partial Differentiation

##### Applications of Partial Differentiation , Expansion of Functions

##### Indeterminate Forms, Numerical Solutions of Transcendental Equations and System of Linear Equations

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