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 I: Click here for the PDF file.
Exercise Set II: Click here for the PDF file.
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 inequalityThird 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.