ME 681: Mathematics for Engineers

Instructor: Anurag Gupta (ag@)

Teaching assistants: Animesh Pandey, Manish Singh, Tushar Joshi, Romil

Schedule: TF 2-3:30 pm, L10

Grading policy: HW (20%), MT (30%), Final (50%)

Primary text:

Linear Algebra

[1] Linear algebra and its applications, 4th Edition, G. Strang. [You can easily get a copy of this book, available in Indian edition, either from one of the bookstores in the shopping centre or from one of the online bookstores.]

ODE

[1] An Introduction to Ordinary Differential Equations, by E. A. Coddington

Additional texts:

Linear Algebra

[2] Lectures on linear algebra, I. M. Gelfand (available as a cheap dover edition)

[3] Finite-dimensional vector spaces, P. Halmos (available in Indian edition)

Course notes:

Lecture 1: Linear equations; Gauss elimination; LU decomposition (Ch. 1 of [1])

Lecture 2: Gauss-Jordon method for finding inverse; Vector spaces (Ch.1 and Ch. 2 of [1]; see also Ch. I of [2])

Assignment 1 (due on 17/1/17) Solution

Lecture 3: Basis and coordinates; Subspace; Coordinate transformation; inner produce space (Ch. 2 of [1]; see also Ch. I of [2])

Assignment 2 (due on 24/1/17)  Solution

Lecture 4: Linear transformations (Ch. 2 of [1]; see also Ch. II of [2]

Lecture 5: Eigenvalues and eigenvectors; characteristic polynomial

Lecture 6: Complex inner product spaces; adjoint; self-adjoint transformations

Assignment 3 (due on 31/1/17)  Solution

Lecture 7: Unitary transformation; commutative linear transformations; Diagonalization; Decomposition into positive definite and unitary transformations

Lecture 8: Linear transformations on Real Euclidean spaces; Symmetric transformations; orthogonal transformations and their canonical form

Assignment 4 (due on 07/2/17)  Solution

Lecture 9: General solution to Ax=b; column space, null space, echelon form

Lecture 10: Column space, null space, row space, and left null space

Assignment 5 (due on 17/2/17)  Solution

Lecture 11: Projections and least square method

Lecture 12: Gram-Schmidt process; QR factorization

Assignment 6 (due on 21/2/17)  Solution

Lecture 13: Eigenvalue problem; applications to differential equations and difference equations

Lecture 14: Jordan canonical form of an arbitrary matrix; application to linear ODEs

Assignment 7 (due on 07/3/17)  Solution

Mid-term exam  Solution

Lecture 15: Vector and tensor calculus; fields; differentiability of a scalar field; gradient; directional derivative

Lecture 16: Gradient of vector and tensor fields; divergence; curl; Laplacian

Assignment 8  (due on 21/3/17)  Solution

Lecture 17: Integral theorems; localization theorem; divergence theorem; Stokes theorem; transport theorem

Lecture 18: Introduction to ODEs; linear first order ODEs; linear ODEs with constant coefficients

Assignment 9  (due on 04/4/17)  Solution

Lecture 19: linear ODEs with constant coefficients; second order homogeneous and inhomogeneous equation

Lecture 20: n-th order linear order with constant coefficients

Assignment 10  (due on 18/4/17)  Solution

Lecture 21: Linear ODEs with variable coefficients

Lecture 22: Linear ODEs with regular singular points

Lecture 23: Bessel Equations

Assignment 11