MA 110 - Linear Algebra and Differential Equations, Spring 2026
MA 110 - Linear Algebra and Differential Equations, Spring 2026
Instructor : Chandan Biswas
Office : 202 F, Mathematics Department
Office Phone : +91 2225767485
Email : cbiswas@iitb.ac.in (if you don't hear back within 48 hours please send a reminder)
Schedule : The class meets twice each week,
Section D1 : Monday + Thursday, 2:30 - 3:55 pm
Section D3 : Tuesday + Friday, 3:30 - 4:55 pm
Office Hours : By appointment
Textbook : 1. H. Anton, Elementary Linear Algebra with Applications (8th Edition), John Wiley, 1995.
2. G. Strang, Linear Algebra and its Applications (4th Edition), Thomson, 2006.
3. S. Kumaresan, Linear algebra - A Geometric Approach, Prentice Hall of India, 2000.
4. E. Kreyszig, Advanced Engineering Mathematics (8th Edition), John Wiley, 1999.
5. W. E. Boyce and R. DiPrima, Elementary Differential Equations (8th Edition), John Wiley, 2005.
6. T. M. Apostol, Calculus, Volume 2 (2nd Edition), Wiley Eastern, 1980
Syllabus :
Vectors in R^n, linear independence and dependence, linear span of a set of vectors, vector subspaces of R^n, basis of a vector subspace. Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix. Determinants and rank of a matrix in terms of determinants. Abstract vector spaces, linear transformations, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem. Inner product spaces, Gram-Schmidt process, orthonormal bases, projections and least squares approximation. Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal), algebraic and geometric multiplicity, diagonalization by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms. Exact equations, integrating factors and Bernoulli equations. Orthogonal trajectories. Lipschitz condition, Picard`s theorem, examples of non-uniqueness. Linear differential equations generalities. Linear dependence and Wronskians. Dimensionality of space of solutions, Abel-Liouville formula. Linear ODE with constant coefficients, characteristic equations. Cauchy-Euler equations. Method of undetermined coefficients. Method of variation of parameters. Laplace transform generalities. Shifting theorems.
Course Policy
You are encouraged to attend lectures regularly. You should try to read the book/class notes and do all of the problems. All the relevant class materials and announcements will be posted on Moodle. Please feel free to ask questions during the class and office hours.
Please Note
Tutorials will be used to discuss the homework problems and any other questions that you may have. You are encouraged to attend these.
A pink slip is a must if asking for a make up exam.
No calculators are allowed in the exams.
Grading :
Midterm : 30%
Final exam : 70%.