Mathematics – 1 ( M1 )
February 20, 2021 2021-02-20 16:21Mathematics – 1 ( M1 )
Mathematics – 1 ( M1 )
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Matrices
- Types of Matrices
- Echelon Form – Rank
- Normal Form – Rank
- System of Linear Equations
- Solving Homogeneous equations
- Solving Homogeneous equations – Example 1
- Solving Homogeneous equations – Example 2
- Solving Non-Homogeneous equations – having Unique solution
- Solving Non-Homogeneous equations – having infinite solution
- Gauss elimination method
- Gauss Seidel Iteration Method
- Non Homogeneous Equations
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Eigen Values and Eigen Vectors
- Linear Transformation
- Orthogonal Transformation
- Eigen Values
- Eigenvectors
- Diagonalization of Matrix
- Cayley-Hamilton Theorem
- Cayley-Hamilton Theorem – Finding Inverse of a amtrix
- power of a matrix by Cayley-Hamilton Theorem
- Quadratic forms and Nature of the Quadratic Forms
- Reduction of Quadratic form to canonical forms by Orthogonal Transformation
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Sequences and Series
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Calculus
- Rolle’s theorem
- Rolle’s theorem – Problem 1
- Rolle’s theorem – Problem 2
- Rolle’s theorem – Problem 3
- Lagrange’s Mean value theorem
- Geometrical Interpretation Of Lagrange’s Mean Value
- Lagrange’s Mean Value – Problem 1
- Lagrange’s Mean Value – Problem 2
- Cauchy’s Mean Value Theorem
- Taylor’s Series
- Taylor’s Series – Problem 1
- Taylor’s Series – Problem 2
- Applications of definite integrals to evaluate surface areas
- Applications of definite integrals to evaluate volumes
- Applications of definite integrals (Contd) – 1
- Applications of definite integrals (Contd) – 2
- Improper Integral – 1
- Improper Integral – 2
- Beta Function
- Beta Function – Problem 1
- Beta Function – Problem 2
- Gamma Function – Problem 1
- Gamma Function – Problem 2
- Gamma Function – Problem 3
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Multi-Variable Calculus
- Limit and continuity
- Partial Differentiation – 1
- Partial Differentiation – 2
- Euler’s Theorem
- Euler’s theorem Problem:1
- Euler’s theorem Problem:2
- Euler’s theorem Problem:3
- Total derivative
- Total Derivative Problem 1
- Total Derivative Problem 2
- Total Derivative Problem 3
- Total Derivative Problem 4
- Jacobian
- Maxima and minima of functions of two variables – 1
- Maxima and minima of functions of two variables – 2
- Maxima and minima of functions of three variables using method of Lagrange multipliers
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