Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. It remains the only mainstream textbook that covers sufficient conditions for maxima and minima in higher dimensions. In the classical curriculum, differentials are defined as linear combinations of other differentials. But then later they are also asserted to be products of differentials, without explanation. This edition clarifies, connecting these new objects as they arise. Metrics are a rather fuzzy topic in most texts, leaving the questions that arc length implies hanging. The exploration of these questions leads to new gateway topics, including spherical geometry (as in navigation), and special relativity, which both emerge rather effortlessly once the metric concept is properly in place.
Chapter P: Preliminaries
Chapter 1: Limits and Continuity
Chapter 2: Differentiation
Chapter 3: Transcendental Functions
Chapter 4: More Applications of Differentiation
Chapter 5:Integration
Chapter 6:Techniques of Integration
Chapter 7:Applications of Integration
Chapter 8: Conics, Parametric Curves, and Polar Curves
Chapter 9: Sequence, Series, and Power Series
Chapter 10: Vectors and Coordinate Geometry in 3-Space
Chapter 11: Arc length, Metric Spaces, and Applications
Chapter 12: Vector Functions and Curves
Chapter 13: Partial Differentiation
Chapter 14: Applications of Partial Derivatives
Chapter 15: Multiple Integration
Chapter 16: Vector Fields
Chapter 17: Vector Calculus
Chapter 18: Differential Forms and Exterior Calculus
Chapter 19: Ordinary Differential Equations
