Textbook in PDF format Mathematical Techniques in Chemistry by Joseph B. Dence (1975) is a 460-page comprehensive guide designed for upper-level undergraduates and graduate students, focusing on applying advanced mathematics to physical chemistry. It covers key topics like differential equations, calculus, matrices, and Fourier transforms, with extensive, chemically motivated problem sets. Key Mathematical Topics Covered: Calculus & Functions: Differentiation, integration, and expansions in series. Linear Algebra: Matrices, vectors, and tensors, applied to topics like molecular vibrational frequencies. Differential Equations: Techniques for solving equations common in physical chemistry. Special Functions: Applications of mathematical functions in chemical contexts. Transform Methods: Fourier transforms are included. Key Chemical Applications: Thermodynamics: Includes a "Digression into Thermodynamics" that applies partial differentiation to Maxwell relations. Quantum Mechanics/Spectroscopy: Matrix techniques are applied to calculate vibrational frequencies of small molecules. The text is described as concise and demanding, often serving as a bridge for students moving from introductory courses to advanced physical chemistry