A Course in Mathematical Analysis, Vol. 1: Derivatives and Differentials; Definite Integrals; Expansion in Series; Applications to Geometry (Classic Reprint)

Explore the geometry of surfaces and space with rigorous, classical methods. Build a solid foundation in surface integrals, line complexes, and theorems used in physics.

This edition gathers foundational tools for advanced study in differential geometry and mathematical physics. It emphasizes the links between geometry and analysis, showing how surface integrals, Green’s and Stokes’ theorems, and related concepts illuminate problems in space, curves, and manifolds.

• Learn how to define and compute surface integrals on two-sided surfaces, with attention to orientation and side choice.
• See how line integrals relate to surface integrals through fundamental theorems, and understand their applications to volumes and shapes.
• Explore geometric constructions and theorems that connect curves, planes, and spaces, including how complex and conic relationships arise in space.
• Apply these ideas to classical problems in geometry and physics, with worked examples and exercises to test understanding.