UM 102: Undergraduate Calculus and Linear Algebra, last taught by me in the January Semester of 2015. I shall teach it again in the January semester of 2020.

My office hours for this course are 5:30 PM to 6:30 PM on Tuesdays and Thursdays. The problem sets of 2015 are found below.

Exercise Set III: Click here for the PDF file. It says Problem Set V because it was the fifth problem set in 2014. It is Problem Set III for 2015.

Mid Sem Question paper is here.

Exercise Set IV: Click here for the PDF file. It says Problem set III because it was the third problem set in 2014. It is problem set IV for 2015.

First class: Revision of basics of vector spaces and Rank-Nullity Theorem. Reference: Apostol's Calculus volume I, section 16.3.

Second class: Inner products and Cauchy-Schwarz inequality. Reference: Apostol's Calculus volume I, section 15.10.

Documents: Various proofs of the Cauchy-Schwarz inequality

Third class: Orthogonality, Parseval's formula, Gram-Schmidt process. Reference: Apostol's Calculus volume I, section 15.11 and 15.13.

Fourth class: Gram-Schmidt continued, uniqueness. Projections. Reference: Apostol's Calculus volume I, section 15.14. Documents: Legendre Polynomials notes from a site at Rochester and closer home a very good set of notes from SERC.

Fifth class: Approximation theorem, system of equations. Reference: Apostol's Calculus volume I, section 15.15 and 16.17.

Sixth class: Determinants - motivation through cross product, axiomatic definition. Reference: Apostol's Calculus volume II, most of Chapter 3.

Seventh class: Existence and uniqueness of the determinant function, computations. Some elementary examples. Reference: Apostol's Calculus volume II, most of Chapter 3.

Eighth class: Hermitian operators on an inner product space - orthogonality of eigenvectors corresponding to different eigenvalues, orthonormal eigenbasis. Reference: Apostol's Calculus volume II, first half of Chapter 5.

Ninth class: Diagonalization of hermitian matrices. Reference: Horn and Johnson, Matrix Analysis, second edition, section 2.3.1.

Tenth class: Limit and continuity. Reference: Apostol's Calculus volume II, Section 8.4. Also see Thomas' calculus, section 14.2

Eleventh and Twelfth class: Differentiation in n-dimensial real space. Directional, partial and total derivatives. Existence of total derivative implies continuity. Example that the existence of all directional derivatives does not imply continuity in general. Reference: Apostol's Calculus volume II, Section 8.6 to 8.12.

Thirteenth class: Quiz 1.

Fourteenth class: A sufficient condition for differentiability. Reference: Apostol's Calculus volume II, Section 8.13

Fifteenth class: Chain rule for differentiation - Jacobian. Reference: Apostol's Calculus volume II, Section 8.15

Sixteenth class:

Seventeenth class:

Eighteenth class:

Nineteenth class:

Twentieth class:

Twenty-first class:

Twenty-second class:

Twenty-third class: Ordinary differential equation - first order non-homogeneous.

I taught UM 102 in 2014 too. The course page for that is here. The mid sem paper for 2014 is here.