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
- Row Matrix
- Column Matrix
- Zero or Null matrix
- Square Matrix
- Diagonal Matrix
- Scalar Matrix
- Unit or Identity Matrix
- Upper Triangular Matrix
- Lower Triangular Matrix
- Triangular Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Determinant of a Matrix
- Singular Matrix
- Transpose of a Matrix
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