Calculus I: Differentiation and Integration

Foundational calculus, worked carefully

Calculus I: Differentiation and Integration by Dan Hamilton is a structured, problem-centered calculus text designed to help readers build confidence through methodical practice. Rather than rushing through topics, it stays close to the essentials: sequences and series, differentiation, and integration.

The book’s approach is practical and classroom-friendly. Each chapter develops the material in a clear sequence, with detailed solutions that show how the calculations are handled step by step. That makes it especially useful for readers who want to see not just the answer, but the reasoning behind it.

What the book covers

• Sequences and series, including arithmetic and geometric patterns
• Core differentiation rules and notation
• Implicit differentiation and higher-order derivatives
• Trigonometric, exponential, logarithmic, and hyperbolic differentiation
• L’Hopital’s Rule for indeterminate forms
• Integration by substitution, trigonometric substitution, and partial fractions
• Hyperbolic integration and exercise solutions in the appendix

Built for steady practice

The tone and structure suggest a text aimed at students who benefit from repetition, worked examples, and straightforward explanations. It may also serve well as a review guide or supplemental reference for tutors, teachers, and self-directed learners who want a dependable calculus workbook-style resource.

A focused companion for first calculus study

If you are looking for a grounded introduction to differential and integral calculus with plenty of guided problem solving, this title offers a clear, disciplined path through the subject. It is especially suited to readers who prefer concrete examples over abstract theory.