MA1011

Linear Algebra & Single Variable Calculus

Information

Instructor: Dr Manjil Pratim Saikia

Contact: [email protected] (please only use this email address to send me emails related to this course)

Lecture Time & Place:

Section B (T 1200-1255, W 1200-1255, Th 1100-1155 and F 1200-1255) in Room 7

Section D (T 1400-1455, W 1400-1455, Th 1400-1455 and F 0900-0955) in Room 5

Office Hours: T 1700-1800 and Th 1700-1800 in Faculty Block - II, Office F-7 (also by appointment)

Attendance Policy: Attendance is mandatory, institute policy is minimum 75% continous attendance failing which the student is not allowed to sit in exams. If you have a genuine reason for missing the lectures please talk to me or the HoD as soon as possible (talking just a few weeks before the exam will not be sufficient).

Course Details

Linear Algebra: Systems of linear equations and their solutions; vector space $\mathbb{R}_n$ and its subspaces; spanning set and linear independence; matrices, inverse and determinant; range space and rank, null space and nullity, eigenvalues and eigenvectors; diagonalization of matrices; similarity; inner product, Gram-Schmidt process; vector spaces (over the field of real and complex numbers), linear transformations.

Single Variable Calculus: Convergence of sequences and series of real numbers; continuity of functions; differentiability, Rolle’s theorem, mean value theorem, Taylor’s theorem; power series; Riemann integration, fundamental theorem of calculus, improper integrals; application to length, area, volume and surface area of revolution.

Reading Materials

Textbook: The recommended textbook for the first part is Linear Algebra and its Applications (Fourth Edition) by Gilbert Strang (Wellesley- Cambridge Press, 2009). This book is available in the institute library, a cheap Indian edition is also available to buy online. In addition, Strang’s webpage (link here) has a treasure trove of video lectures and lecture notes on first year undergraduate linear algebra that he has taught for many years at MIT. He also has a very popular OCW which is also worth watching.

For the second part of the course, I will be using my own notes, which I will share in this webpage after the lecture. I still recommend that you follow a book of your choice for the material so that you can practice solving problems. Any of the following books can be choosen for this purpose (the editions selected are the ones to which I have access to, but you can choose any other edition of the books):

  1. An Introduction to Calculus and Real Analysis (1st ed.), Sudhir R. Ghorpade and Balmohan V. Limaye, Springer, 2006.
  2. Introduction to Real Analysis (4th ed.), Robert G. Bartle and Donald R. Sherbert, John Wiley & Sons, 2011.
  3. Understanding Analysis (2nd ed.), Stephen Abott, Springer, 2015.

Class Notes

Linear Algebra

Review of solving simultaneous linear equations
Lecture 7
Lecture 8
Lecture 9
Determinants
Orthogonality
Gram-Schmidt Process
Eigenvalues & Eigenvectors
Similarity & Diagonalization
Linear Transformations

Single variable Calculus

Fundamental Functions and their Graphs
Limits of Sequences
Convergence of Series
Infinite Series
Supremum & Infimum
Continuity of Functions
Differentiability
Theorems for Differentiable Functions
Higher Order Derivatives
Fundamental Theorem of Calculus

Problem Sheets

Linear Algebra

Sheet 1 (Vector Spaces)
Sheet 2 (Matrices)
Sheet 3 (Linear Independence, Basis & Dimension)
Sheet 4 (Programming)
Sheet 5 (Determinants)
Sheet 6 (Inner Products & Orthogonality)
Sheet 7 (Eigenvalues & Eigenvectors)
Sheet 8 (Linear Maps)

Single variable Calculus

Sheet 9 (Continuity)
Sheet 10 (Differentiability)

Exams

Assessment I
Assessment II