## Mathematics in Engineering-I

Semester: Spring

Offered: 2013

Offered at Princeton University

**Course outline:** A treatment of the theory and applications of ordinary differential equations with an introduction to partial differential equations. The objective is to provide the student with an ability to solve problems in this field.

## Chemical Process Calculations

Semester: Fall

Offered: 2009

Offered at IIT Gandhinagar

**Course Outline:** Basic problem solving skills in Chemical Engineering; Unit conversions, Stoichiometry; material and energy balances; material and energy balances with chemical reactions; purge and recycle; thermophysics and thermochemistry; first law of thermodynamics and its applications.

## Linear Algebra

Semester: Spring

Offered: 2009

Offered at IIT Gandhinagar

**Course outline:**Vectors in Rn; Vector subspaces of Rn; Basis of vector subspace; Systems of Linear equations; Matrices and Gauss elimination; Determinants and rank of a matrix; 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; Multiplicity.

## Ordinary Differential Equations

Semester: Spring

Offered: 2009

Offered at IIT Gandhinagar

**Course Outline: **Exact equations, Integrating factors and Bernoulli’s equation; Orthogonal trajectories; Lipschitz condition, Picard’s theorem; Wronskians; Dimensionality of space of solutions, Abel-Liouville formula; Linear ODE’s with constant coefficients; Cauchy-Euler equations; Method of undetermined coefficients; Method of variation of parameters; Laplace transforms, Shifting theorems, Convolution theorem.