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.

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

Homework-4 HW-4.pdf

Lecture 11: Basis and dimension

Suggested reading: Kolman and Hill, Section 4.6

Lecture 12: Linear transformations and the standard matrix corresponding to a linear transformation, null spaces and rank spaces, rank-nullity theorem.

Suggested reading: Kolman and Hill, Sections 6.1, 6.2, 6.3

Homework-5 HW-5.pdf

Lecture 13: Collegiate Learning Assessment (CLA-1)

Mid-term exam

Lecture 14: Eigenvalues of a linear map and eigenvectors of a linear map associated with their respective eigenvalues. Eigenspaces of a linear map associated with the eigenvalues.

Suggested reading: Kolman and Hill, Sections 7.1, 7.2

Lecture 15: Diagonalizable matrices.

Suggested reading: Kolman and Hill, Sections 7.2

Homework-6 HW-6.pdf

Lecture 16: Collegiate Learning Assessment (CLA-2)

Lecture 17: Basic notions of Differential equations.

Lecture notes: intro-ODEs.pdf

Lecture 18: Direct integration for solving the ODEs and separable ODEs

Lecture notes: separable-ODEs.pdf

Lecture 19: First-order linear differential equations and Bernoulli equations

Lecture notes: first-order-lin-diff-equ.pdf, Bernoulli-equ.pdf 

Homework-7 HW-7.pdf

Lecture 20: Exact differential equations

Lecture notes: exact-diff-equ.pdf

Lecture 21: Non-exact differential equations, integrating factors for non-exact equations

Lecture notes: non-exact-diff-equ.pdf

Lecture 22: Collegiate Learning Assessment (CLA-3)

Lecture 23: Homogeneous equations and exactness

Lecture notes: homo-equ-exactness.pdf

Lecture 24: Second-order linear differential equations, Wronskian determinants.

Lecture notes: homo-2nd-order-lin-diff-equ.pdf

Lecture 25: Method of order of reductions.

Lecture notes: order of reductions.pdf

Lecture 26: Constant-coefficient homogeneous 2nd-order linear differential equations.

Lecture notes: const-coeff-homo-lin-diff-equ.pdf

Lecture 27: Non-homogeneous 2nd-order linear differential equations.

Lecture notes: non-homo-2nd-order-lin-diff-equ.pdf

Lecture 28: Second-order linear non-homogeneous differential equations. Variation of parameters

Lecture notes: variation-of-parameters.pdf

Lecture 29: System of first-order differential equations, and Solution of a homogeneous constant coefficient system of differential equations 

Lecture notes: system of first-order ODEs.pdf

Lecture 30: Converting higher-order differential equations into a system of equations 

Lecture notes: higher-order ODEs into system.pdf

End-term exam