Linear Algebra and Ordinary Differential Equations (FIC 117)

Textbooks: 

• Kolman and Hill, Elementary Linear Algebra with Applications, 9th Edition, Pearson, 2008.

• Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley 2020

Reference Books: 

• Stephen H Friedberg, Arnold J Insel, Lawrence E. Spence, Linear Algebra. 4th Edition, Pearson, 2006.

Lecture notes: Available HERE

Topics covered:

Lecture 1:  Algebraic Properties of Matrix Operations

Suggested reading: Kolman and Hill, Sections 1.2, 1.3, 1.4, 1.5

Lecture 2: Echelon form of matrices and the rank of matrices.

Suggested reading: Kolman and Hill, Sections 2.1, 2.2

Lecture 3: System of linear equations by using the Gauss elimination method.

Suggested reading: Kolman and Hill, Sections 2.1, 2.2

Lecture 4: System of linear equations by using the Gauss elimination method (contd.).

Suggested reading: Kolman and Hill, Sections 2.1, 2.2

Homework-1 HW-1.pdf

Lecture 5: Elementary matrices and the inverse of a matrix by using Elementary Row Operations

Suggested reading: Kolman and Hill, Section 2.3

Lecture 6: Determinants and their properties

Suggested reading: Kolman and Hill, Sections 3.1, 3.2, 3.3, 3.4

Homework-2 HW-2.pdf

Lecture 7: Vectors in the Plane and in 3-Space, Vector Spaces

Suggested reading: Kolman and Hill, Sections 4.1, 4.2

Lecture 8: Subspaces of a vector space

Suggested reading: Kolman and Hill, Section 4.3

Homework-3 HW-3.pdf

Lecture 9: Linear Combination and Span

Suggested reading: Kolman and Hill, Section 4.4

Lecture 10: Linear dependence

Suggested reading: Kolman and Hill, Section 4.5