QE104: Mathematics II
| Course Number : QE104
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| Course Title : Mathematics II
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| Credits : 3
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| No
| Course Content
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| Time Allocated (hours) |
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| L
| T
| O
| A |
| 01
| Vectors
- Review on vectors in 2-D
- Vectors in 3-D
- Vectors algebra
- Vectors calculus
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| 02
| Matrix Theory
- Introduction
- Basic algebraic operations of addition and multiplication
- Types of matrices (Symmetric, Triangular, Orthogonal etc.); Transpose, Adjoint and Inverse of a matrix
- Partitioning of matrices
- Inverse by partitioning
- Elementary and Echelon matrices
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| 10
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| 5
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| 03
| Determinants
- Definition; Minus and Cofactors
- Elementary row-column operations on determinants
- Expansion of determinants
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| 3
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| 2
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| 04
| Transformations
- Linear Transformations
- Elementary Transformations
- Rank of a matrix
- Theorems on rank
- Rank and Echelon matrices
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| 2
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| 1
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| 05
| Solution of Simultaneous Equations
- Matrix representation, homogenous and non-homogenous systems
- Conditions for unique solution and infinite number of solutions
- Cramer's rule
- Gussian elimination
- Gauss-Jordan form
- Triangular factorization
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| 4
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| 2
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| 06
| Vector Space
- n-D vectors and vector spaces
- Linear dependence and independence
- Spanning sets and basis
- Changing of bases; Orthogonal bases
- Schmidt orthogonalization process
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| 4
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| 2
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| 07
| Characteristic Value Problems
- Eigen values
- Eigen vectors and properties
- Cayley-Hamilton theorem
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| 5
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| 2
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| 08
| Quadratic Forms
- Diagonalization of quadratic forms
- Simultaneous diagonalization of quadratic forms
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| 3
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| 2
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| Total
=36+18=54 |
| 36
| 0
| 0
| 18
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| Assessment
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| Percentage
| Marks
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| Continuous Assessment
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| 10
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| Assignment |
| 10
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| Course Work |
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| Written Examinations
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| 90
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| Mid-semester
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| 30
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| End-semester
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| 60
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