Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.

Coordinates and Calculus.- Coordinate Systems and Vectors.- Differentiation.- Integration: Formalism.- Integration: Applications.- Dirac Delta Function.- Algebra of Vectors.- Planar and Spatial Vectors.- Finite-Dimensional Vector Spaces.- Vectors in Relativity.- Infinite Series.- Infinite Series.- Application of Common Series.- Integrals and Series as Functions.- Analysis of Vectors.- Vectors and Derivatives.- Flux and Divergence.- Line Integral and Curl.- Applied Vector Analysis.- Curvilinear Vector Analysis.- Tensor Analysis.- Complex Analysis.- Complex Arithmetic.- Complex Derivative and Integral.- Complex Series.- Calculus of Residues.- Differential Equations.- From PDEs to ODEs.- First-Order Differential Equations.- Second-Order Linear Differential Equations.- Laplace's Equation: Cartesian Coordinates.- Laplace's Equation: Spherical Coordinates.- Laplace's Equation: Cylindrical Coordinates.- Other PDEs of Mathematical Physics.- Special Topics.- Integral Transforms.- Calculus of Variations.- Nonlinear Dynamics and Chaos.- Probability Theory.