Vector Calculus And Linear Algebra
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Vector Calculus And Linear Algebra Syllabus — Unit-wise Content
The official GTU curriculum for Vector Calculus And Linear Algebra (subject code 2110015) as prescribed for ETC · Semester 1 divides the course into 6 units, covering 11 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (2110015)Unit 1 Systems of Linear Equations and Matrices
- Systems of Linear Equations Matrices and Elementary Row Operations The Inverse of a Square Matrix Matrix Equations Applications of Systems of Linear Equations 5 14-16%
Unit 2 Linear Combinations and Linear Independence
- Vectors inn R . Linear Combinations Linear Independence Vector Spaces Definition of a Vector Space Subspaces Basis and Dimension Coordinates and Change of Basis 7 20-22%
Unit 3 Linear Transformations 7 20-22%
- VECTOR CALCULUS AND LINEAR ALGEBRA Linear Transformations The Null Space and Range Isomorphisms Matrix Representation of Linear Transformations Similarity Eigenvalues and Eigenvectors Eigen values and Eigen vectors Diagonalization
Unit 4 Inner Product Spaces
- The Dot Product onn R and Inner Product Spaces Orthonormal Bases Orthogonal Complements Application: Least Squares Approximation Diagonalization of Symmetric Matrices Application: Quadratic Forms 6 18-20%
Unit 5 Vector Functions
- Vector & Scalar Functions and Fields
- Derivatives Curve
- Arc length
- Curvature & Torsion Gradient of Scalar Field
- Directional Derivative Divergence of a Vector Field Curl of a Vector Field 5 14-16%
Unit 6 Vector Calculus
- Line Integrals Path Independence of Line Integrals Green`s Theorem in the plane Surface Integrals Divergence Theorem of Gauss Stokes`s Theorem 6 18-20% Note: Teachers are advised to encourage students to perform the projects in group of 4 students for conceptual understanding by geometrically
- numerically and algebraically
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