This is the webpage of UM 102/UMA 102: Undergraduate Calculus and Linear Algebra, in the January semester of 2025.

The office hour for this course is 5:30 PM to 6:30 PM in the evening. Do drop me a mail in the morning if you want to meet me that evening.

Exercise Set I: Click here for the PDF file.

First and second classes: Revision of basics of vector spaces, Inner products and Cauchy-Schwarz inequality, Rank-Nullity Theorem. Reference: Apostol's Calculus volume I, sections 15.10 and 16.3.

Third class: Orthogonality. Gram-Schmidt process. Self-adjoint matrices. Projection onto a subspace. Reference: Apostol's Calculus volume I, sections 15.11, 15.13, 15.14, 15.15 and 16.17.

Exercise Set II: Click here for the PDF file.

Fourth class: Determinants. Reference: Apostol's Calculus volume II, Chapter 3. See also Chapter 4 of this book.

Fifth class: Determinants. Reference: this good note.

Exercise Set III: Click here for the PDF file.

Sixth class: Eigenvalues. Reference: Apostol's Calculus volume II, Chapter 4. Diagonalization of normal matrices. A proof different from the one done in class.

Exercise Set IV: Click here for the PDF file.

Seventh, eigth and ninth class: Multivariable Calculus. Reference: Apostol's Calculus volume II, Chapter 8.