Chapter Outline

This chapter provides a brief overview of partial differential equations, which involve partial derivatives of a function with respect to multiple independent variables.

7.1 Introduction: This section outlines boundary and initial conditions, essential for solving initial boundary value problems in PDEs.

7.2 Fourier Series: This section reviews the Fourier Series, a crucial tool for expressing the solution of partial differential equations.

7.3 Heat Equation: This section discusses using the method of Separation of Variables for solving the heat equation, which describes how heat diffuses through a medium over time.

7.4 Wave Equation: This section briefly discusses the solution to the wave equation, which models the propagation of waves, such as sound and light waves, through a medium

Pioneers of Progress

Maryam Mirzakhani, born in 1977 in Tehran, Iran, was a trailblazing mathematician whose profound contributions to geometry and dynamical systems reshaped our understanding of these fields. Her mathematical journey, which began with outstanding successes in the International Mathematical Olympiads, culminated in her earning the prestigious Fields Medal in 2014, making her the first woman to receive this honor. Mirzakhani’s groundbreaking work at Harvard University under Curtis McMullen focused on the intricate geometry of Riemann surfaces and their moduli spaces, encompassing areas like hyperbolic geometry and Teichmüller theory. Renowned for her deep, creative thinking and ability to draw connections between different mathematical areas, Mirzakhani not only solved long-standing problems but also inspired a generation, particularly women and girls in STEM, through her remarkable intellect and perseverance. Her legacy as a symbol of intellectual curiosity and boundary-breaking achievement makes her an exemplary figure for illustrating the far-reaching impact and significance of mathematical concepts.