Vector Calculus: Vector Function. Derivative of a Vector function. Gradient of a scalar function. Divergence and curl of vector functions. Directional derivative and calculation of pressure, Kinetic interpretation of energy.Linear Algebra: integral of matrices. Addition and multiplication of matrices. Inverse of square matrix. Orthogonal, Hermition and Unitary matrices. Properties of determinants and expansion of the determinants. Solution of nonhomogeneous linear equations by Cramer’s rule. Elementary operations. Echelons and reduced echelon forms. Rank of a matrix. Equivalent matrices. Gauss-Jordan elimination method. System linear homogeneous and nonhomogeneous equations vector spaces. Subspaces. Linear dependence and independence Span, Basis and Dimension. Eigen value problems Eigen vectors. Cayley - Hamilton theorem.
Intended learning outcomes
By the end of the course, the student must be able to:
explain the basic concepts of arrays and their types and operations.
discuss class operations on matrices and scalar and reduced matrices.
perform operations on matrices and methods for finding the inverse of a matrix.
describe determinants and their use in finding the inverse of a square matrix determinants are used to find the inverse of a matrix.
use matrices to solve systems of linear equations.
apply determinants in solving systems of linear equations.
discuss the solution of a system of linear equations using determinants
Teaching and learning methods
The course will be presented to the student through a combination of theoretical lectures, panel discussions, solving exercises, and discussion and dialogue.
Methods of assessments
semester work = 40
final = 60
Course contents
Week 1: Matrices
Week 2: Matrices Types
Week 3: Operations on Matrices
Week 4: Class operations on matrices
Week 5: Inverse Matrix
Week 6: The concept of determinants
Week 7: Specifications
Week 8: Specifications
Week 9: Find the inverse matrix using the selectors
Week 10: Resolve the linear equation system
Week 11: Resolve linear equation system using matrices
Week 12: Resolve linear equation system using matrices
Week 13: Resolution of linear equation system using determinants
Week 14: Resolve linear equation system using determinants
