Introduction to differential calculus

Introduction:

“Introduction to Differential Calculus” by Ulrich L Rohde is a concise and accessible introduction to differential calculus. The book is intended for students who are new to calculus and want to learn the basics of differential calculus. The author has presented the material in a clear and concise manner, making it easy for students to follow.

Overview of the Book:

The book is divided into ten chapters, each covering a different aspect of differential calculus. The first chapter provides an introduction to calculus and covers the basic concepts of functions, limits, and derivatives. The next few chapters focus on differentiation rules, applications of derivatives, and optimization problems.

One of the strengths of the book is the numerous examples and exercises provided throughout each chapter. The author has carefully selected examples that illustrate the key concepts and ideas in each chapter, making it easy for students to apply what they have learned. Additionally, the exercises are designed to challenge students and reinforce their understanding of the material.

Chapter Breakdown:

Chapter 1: Introduction to Calculus –

The chapter introduces the basic concepts of functions, limits, and derivatives. The author also provides an overview of the history of calculus.

Chapter 2: Differentiation Rules –

This chapter covers the various rules for finding derivatives of functions. The author explains the power rule, product rule, quotient rule, and chain rule, and provides numerous examples to illustrate each rule.

Chapter 3: Applications of Derivatives –

This chapter focuses on the various applications of derivatives, such as finding maxima and minima, concavity and inflection points, and related rates problems.

Chapter 4: Optimization Problems –

This chapter covers optimization problems, including finding the maximum or minimum value of a function subject to certain constraints.

Chapter 5: Higher Order Derivatives –

The chapter introduces the concept of higher order derivatives and provides examples to illustrate how they are use.

Chapter 6: Implicit Differentiation –

This chapter covers implicit differentiation, which is use to find the derivative of functions that are not express explicitly.

Chapter 7: Logarithmic Differentiation –

This chapter covers logarithmic differentiation, which is use to simplify the process of finding the derivative of complicated functions.

Chapter 8: Exponential and Logarithmic Functions –

This chapter covers exponential and logarithmic functions, including their properties and derivatives.

Chapter 9: Inverse Functions –

The chapter covers inverse functions, including their properties and derivatives.

Chapter 10: Parametric Equations –

This chapter covers parametric equations, which are use to describe curves in the plane.

Final Thoughts:

Overall, “Introduction to Differential Calculus” by Ulrich L Rohde is an excellent introduction to differential calculus. The author has presented the material in a clear and concise manner, making it easy for students to follow. The numerous examples and exercises provided throughout each chapter help students to apply what they have learned and reinforce their understanding of the material.

Strengths

One of the strengths of the book is its organization. The author has divided the material into ten chapters, each covering a different aspect of differential calculus. This makes it easy for students to focus on specific topics and to review specific concepts as needed.

Conclusion

I would highly recommend “Introduction to Differential Calculus” to anyone who is new to calculus and wants to learn the basics of differential calculus. The book is well-written, accessible, and provides a solid foundation in the subject.