Differential and Integral Calculus by Feliciano and Uy: A Review
Differential and integral calculus are two branches of mathematics that deal with the study of rates of change, functions, curves, areas, volumes, and other concepts. A comprehensive and rigorous textbook on these topics is Differential and Integral
Calculus by Feliciano and Uy, which was published in 2010 by C & E Publishing, Inc.

The book covers the basic concepts and techniques of differential and integral calculus, as well as some applications to physics, engineering, economics, and geometry. It also includes numerous examples, exercises, and problems that help students develop
their skills and understanding. The book is divided into 12 chapters, each with an introduction, objectives, definitions, theorems, proofs, examples, exercises, problems, and summaries. The chapters are:

differential and integral calculus by feliciano and uy
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Chapter 1: Limits
Chapter 2: Continuity
Chapter 3: Derivatives
Chapter 4: Applications of Derivatives
Chapter 5: Integration
Chapter 6: Applications of Integration
Chapter 7: Techniques of Integration
Chapter 8: Improper Integrals
Chapter 9: Differential Equations
Chapter 10: Infinite Series
Chapter 11: Conic Sections
Chapter 12: Polar Coordinates and Parametric Equations

The book is suitable for college students who are taking a course in differential and integral calculus. It is also a useful reference for teachers, researchers, and professionals who need to use calculus in their work. The book assumes that the readers
have some background in algebra, trigonometry, and analytic geometry. The book also provides some review materials on these topics in the appendices.

The book is well-written, clear, and concise. It explains the concepts and methods in a logical and systematic way. It also provides proofs for the main results and shows how they are derived from the definitions and axioms. The book uses a variety of
examples to illustrate the concepts and techniques. The examples range from simple to complex, from theoretical to practical, and from classical to modern. The book also provides exercises and problems that test the students' comprehension and
application of the topics. The exercises and problems are classified into three levels of difficulty: easy, moderate, and difficult. The book also provides answers to some of the exercises and problems at the end of each chapter.

The book is well-organized, comprehensive, and rigorous. It covers all the essential topics of differential and integral calculus in a coherent and consistent manner. It also integrates some applications of calculus to various fields of science and
engineering. The book is a valuable resource for students who want to learn calculus in depth and for teachers who want to teach calculus effectively.


One of the strengths of the book is its clarity and precision. The book uses a consistent notation and terminology throughout the chapters. It also defines and explains the concepts and terms in a clear and precise way. The book avoids unnecessary jargon
and ambiguity that might confuse the readers. The book also provides proofs for the main results and shows how they are derived from the definitions and axioms. The proofs are logical and rigorous, but also concise and easy to follow.

Another strength of the book is its comprehensiveness and depth. The book covers all the essential topics of differential and integral calculus in a coherent and consistent manner. It also integrates some applications of calculus to various fields of
science and engineering. The book provides a solid foundation for students who want to learn calculus in depth and for teachers who want to teach calculus effectively. The book also prepares the students for more advanced courses in mathematics, such as
analysis, differential equations, and complex analysis.

A third strength of the book is its variety and richness. The book uses a variety of examples to illustrate the concepts and techniques. The examples range from simple to complex, from theoretical to practical, and from classical to modern. The examples
show how calculus can be used to solve problems in physics, engineering, economics, geometry, and other disciplines. The book also provides exercises and problems that test the students' comprehension and application of the topics. The exercises and
problems are classified into three levels of difficulty: easy, moderate, and difficult. The exercises and problems are challenging but not overwhelming. They help the students develop their skills and understanding.



One of the weaknesses of the book is its length and density. The book is quite long and dense, with 12 chapters and over 800 pages. It might be difficult for some students to read and digest all the material in one semester. It might also be hard for
some teachers to cover all the topics in one course. The book might require more time and effort from both the students and the teachers than other textbooks on calculus.

Another weakness of the book is its lack of color and graphics. The book is mostly black-and-white, with only a few diagrams and graphs. It might be boring for some readers who prefer more color and graphics in their textbooks. It might also be less
effective for some learners who rely on visual aids to understand the concepts. The book might benefit from more color and graphics to make it more appealing and engaging.

A third weakness of the book is its limited accessibility and availability. The book is published by a local publisher in the Philippines, which might make it hard to find or order in other countries. It might also be expensive for some students who have
limited budgets. The book might not be widely used or recognized by other institutions or instructors who teach calculus.

In conclusion, Differential and Integral Calculus by Feliciano and Uy is a well-written, clear, comprehensive, rigorous, varied, and rich textbook on differential and integral calculus. It is suitable for college students who are taking a course in
differential and integral calculus. It is also a useful reference for teachers, researchers, and professionals who need to use calculus in their work. However, the book also has some weaknesses, such as its length, density, lack of color, graphics,
accessibility, and availability. Therefore, potential readers should consider these factors before choosing this book as their textbook or reference.
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