UM 102: Analysis and Linear Algebra II

Course Syllabus

Linear Algebra continued: Inner products and Orthogonality; Determinants; Eigenvalues and Eigenvectors; Diagonalisation of Symmetric matrices. Multivariable calculus: Functions on $R^n$

Partial and Total derivatives; Chain rule; Maxima, minima and saddles; Lagrange multipliers; Integration in $R^n$, change of variables, Fubini's theorem; Gradient, Divergence and Curl; Line and Surface integrals in $R^2$ and $R^3$ ; Stokes, Green's and Divergence theorems.

Introduction to Ordinary Differential Equations; Linear ODEs and Canonical forms for linear transformations.

Assignments

Assignments will be posted roughly once a week.

• Dynamics with complex Eigenvalues, due by Mon, 16 Apr 2018.
• Differential forms and holomorphic functions, due by Mon, 02 Apr 2018.
• Multiple and Line Integrals, due by Mon, 26 Mar 2018.
• Lagrange Multipliers, due by Mon, 19 Mar 2018.
• Differentiability, due by Mon, 12 Mar 2018.
• Nilpotent Linear transformations, due by Mon, 12 Feb 2018.
• Left and Right Inverses, due by Mon, 05 Feb 2018.
• Determinants, due by Mon, 29 Jan 2018.
• Orthogonal polynomials and functions, due by Mon, 22 Jan 2018.
• Norms and Inner products, due by Fri, 12 Jan 2018.

Suggested books

1. T. M. Apostol, Calculus, Volume II, 2nd. Edition, Wiley Wiley India, 2007.
2. Kalyan Mukherjea, Differential Calculas in Normed Linear Spaces (Texts and Readings in Mathematics), Hindustan Book Agency, 2007.
3. G. Strang, Linear Algebra And Its Applications, 4th Edition, Brooks/Cole, 2006
4. M. Artin, Algebra, Prentice Hall of India, 1994.
5. M. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd Edition, Academic Press, 2004.

Course Details

• Instructor: Siddhartha Gadgil
• E-mail: siddhartha.gadgil@gmail.com.
• Office: N-15, Department of Mathematics.
• Timing:
  • Lectures: Mon-Wed-Fri: 9:30 a.m. to 10:30 a.m.
  • Tutorials: Mon: 12:00 noon - 1:00 p.m.
• Lecture Venue: Undergraduate main lecture hall
• Teaching Assistants:
  • Abu Sufian (group A); office: N-07.
  • Anindya Biswas (group B); office: R-22; office hours: Fri 9:00 pm to 10:00 pm.
  • G. V. K. Teja (group C); office: R-21.
  • Prateek Vishwakarma (group D); office: R-24.
  • Amardeep Sarkar (co-ordinator); office: L-12.