Calculus and Applications Spring 2023 - Indicative syllabus

Below is the range of topics covered in the course; it may change from year to year.

Syllabus:

• Fourier Transforms: Exponential, cosine, and sine transforms; elementary properties; convolution theorem; energy theorem.
• Ordinary Differential Equations: Introduction, solutions for first and second order ODEs, linear ODEs, separable, homogeneous, linear equations; special cases; linear higher-order equations with constant coefficients; systems of constant-coefficient linear ODEs; qualitative analysis of linear and nonlinear ODEs, phase plane analysis, stability, bifurcation analysis; examples from Newtonian dynamics.
• Introduction to Multivariable Calculus: General properties of functions of several variables, partial and total derivatives, second-order derivatives, condition for equality of mixed partial derivatives, Taylor expansions, chain rule, change of variables including planar polar coordinates.