Mathematics II (MTH168) — Notes, Syllabus & Past Questions

Advanced calculus and linear algebra for solving complex computational problems.

Core Course10 Chapters

Linear Equations in Linear Algebra

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix equations Ax = b, Applications of linear system, Linear independence.

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Chapter 29 Pages

Transformation

Introduction to linear transformations, the matrix of a linear Transformation, Linear models in business, science, and engineering.

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Chapter 312 Pages

Matrix Algebra

Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Partitioned matrices, Matrix factorization, The Leontief input output model, Subspace of Rn, Dimension and rank.

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Chapter 412 Pages

Determinants

Introduction, Properties, Cramer's rule, Volume and linear transformations.

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Chapter 511 Pages

Vector Spaces

Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly independent sets: Bases, Coordinate systems.

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Chapter 68 Pages

Vector Space Continued

Dimension of vector space and Rank, Change of basis, Applications to difference equations, Applications to Markov Chains.

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Chapter 711 Pages

Eigenvalues and Eigen Vectors

Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and linear transformations, Complex eigenvalues, Discrete dynamical systems.

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Chapter 810 Pages

Orthogonality and Least Squares

Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The GramSchmidt process, Least squares problems, Application to linear models, Inner product spaces.

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Chapter 98 Pages