Waqas Ali Azhar - Linear Algebra with introduction to Differential Equations

This is the first course of a two semester sequence in linear algebra. This course gives a working knowledge of: systems of linear equations, matrix algebra, determinants, eigenvectors and eigenvalues, finite-dimensional vector spaces, matrix representations of linear transformations, matrix diagonalization, changes of basis, Separable and first-order linear equations with applications, 2nd order linear equations with constant coefficients, method of undetermined coefficients, Systems of linear ODE's with constant coefficients, Solution by eigenvalue/eigenvectors, Non homogeneous linear systems.

Class Schedule: M, W 17:00-18:15 (Acad Block A13)

Office Hours: M, W 11:00-13:00. (SSE- MATH 9B30)

TAs Office Hours: Check LMS (https://lms.lums.edu.pk/)

Resources:

For resources click here.

Quizzes with solutions

Quizzes with solutions can be found here. For S1-S2 Quizzes click here.

Weekly Breakdown:

[Week 1] Linear systems, Matrices, and their properties, Solution of a linear system.

[Week 2] Geometry of solutions of a linear system, Echelon and Reduced Echelon Forms, Gauss and Gauss Jordan Elimination methods.

[Week 3] Matrix operations, Transpose and Trace of a matrix, Inverse of a matrix, Computing inverse of a 2x2 system.

Quiz 1 (6-02-23)

[Week 4] Cramer's rule, Inverse of an nxn matrix.

[Week 5] Determinants, Properties of determinants, Singular matrices.

[Week 6] Homogenous and Non-homogenous systems.

Quiz 2 (27-02-23)

[Week 7] Vector in Rn, Vector operations, vector (inner) products in n-space, Norms.

[Week 8] Real vector space, Subspaces, Dimension and Bases.

Midterm (24-03-23)

Midterm Key

[Week 9] Linear Transformations, Matrix of a linear Transformation, Composition of Transformations.

[Week 10] Invertible Linear Transformations, Kernel and Range, Row-space, Column space.

[Week 11] Rank and nullity theorem, Eigenvalues, Eigenvectors, Defective matrices and Diagonalization, Similar matrices.

Quiz 3 (05-12-23)

[Week 12] Introduction to Differential equations, Basic notions, First order ODE.

[Week 13] Separable, Linear, Bernoulli, Homogenous, substitution method and exact ODE.

Quiz 4 (19-12-23)

[Week 14] System of first order Differential equations and their solutions using eigenvalues and eigenvectors.

Ex-Lec P1 (Zoom Recording)

Ex-Lec P2 (Zoom Recording)

Ex-Lec Notes

Final Exam (04-05-23)

Final Exam Key