Mathematical concepts in trigonometry, exponentiation, differentiation, and integration are explored through real-life examples. The authors then use these examples to illustrate a direct application of these areas of mathematics to complex Fourier analysis. This resource provides insight into the development of mathematical understanding through the eyes of students. Mathematics 10 - Foundations and Pre-calculus (2010). Mathematics 20 - Foundations (2010). Mathematics 20 - Pre-calculus (2010). Mathematics 30 - Pre-calculus (2012).