This course provides additional mathematical techniques and deepens the understanding of concepts in mathematics to support continued study in environmental engineering. Emphasis is placed upon using mathematics to gain insight into natural and man-made phenomena that give rise to problems in differential equations and vector calculus. Calculus study focuses on vector fields, differential operators, and the vector integral theorems. This material is then used to derive the diffusion equation. Solutions of this equation via Fourier series, separation of variables, and numerical methods are then studied.