Review: "Differential Calculus" by Feliciano Uy
Differential Calculus Scope
: Covers fundamental concepts including limits, continuity, and derivatives. Key chapters detail differentiation of algebraic and transcendental functions, applications like curve sketching and optimization, indeterminate forms, and derivatives from parametric equations.
Chapter 3: Applications of the Derivative
– This is a favorite among engineering students. It covers real-world modeling problems such as related rates, curve sketching, and calculating the absolute maxima and minima of functions.
- The "Schaum's Outline" Series: Very similar problem-solution format.
- The "Silverio" Books: Another Filipino author, slightly easier than Uy. Read Silverio first, then tackle Uy for mastery.
- LibreTexts (OpenStax): Free, legal, online calculus textbooks. While not Uy, they cover the same topics with interactive graphs.
Chapter 7: Parametric Equations & Curvature
– This covers finding derivatives from parametric equations as well as calculating the radius and center of curvature for various curves.
Chapter 2: Differentiation of Algebraic Functions
– Introduction to the derivative, geometric significance, power rules, the chain rule, and implicit differentiation.
Accessibility
: Uses simple, direct language to demystify complex theorems.