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.

1.: 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.

Documents: Various proofs of the Cauchy-Schwarz inequality

2.: 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.

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

4.: Determinants. Reference: this good note.

Exercise Set III: Click here for the PDF file.

5.: 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.

6.: Multivariable Calculus. Reference: Apostol's Calculus volume II, Chapter 8.

 

Exercise Set V: Click here for the PDF file.

The mid term examination on 17 02 2025.

7.: Multivariable Calculus. Jacobians. Reference: Apostol's Calculus volume II, Chapter 8. Sections 8.18 to 8.22.

8.: Multivariable Calculus. Implicit DIfferentiation Reference: Apostol's Calculus volume II, Chapter 9. Sections 9.6 to 9.8.

9.: Maxima, minima and saddle points: Apostol's Calculus volume II, Chapter 9. Sections 9.9 to 9.12.

Exercise Set VI: Click here for the PDF file.

10.: Line Integral. Reference: Apostol's Calculus volume II, Chapter 10. Sections 10.1, 10.2, 10.3, 10.4, 10.10. 10.11, 10.14, 10.15, 10.16.

Exercise Set VII: Click here for the PDF file.

11.: Multiple integral. Reference: Apostol's Calculus volume II, Chapter 11. Sections 11.6 to 11.15 and 11.19 to 11.22.

Exercise Set VIII: Click here for the PDF file.

12.: Multiple integral - change of variable. Reference: Apostol's Calculus volume II, Chapter 11. Sections 11.26 to 11.28.

13. ODE: Sections 7 - 10 of Simmons, Differential Equations with Applications and Historical Notes, Third Edition.

Exercise Set IX: Click here for the PDF file.