Math 209: Differential equations

This course provides a rigorous and practical introduction to core topics in analysis and applied mathematics. We begin with the definition of the limit of a sequence and fundamental properties of convergence and divergence. Building on this, we study infinite series and standard convergence tests. We then develop the representation of functions by power series, with emphasis on Taylor and Maclaurin expansions and their error estimates. The course introduces Fourier series for periodic functions and the Fourier integral for nonperiodic signals. In multivariable calculus, we cover partial derivatives of functions of two variables and basic differentiation rules. Finally, we treat first-order differential equations and selected applications to modeling in the physical and natural sciences.