Difference Equations to Differential Equations by Dan Sloughter
Difference Equations to Differential Equations - Table of Contents
1. Sequences, Limits, and Difference Equations
2. Calculus: Areas and Tangents
3. Sequences
4. The Sum of a Sequence
5. Difference Equations
6. Nonlinear Difference Equations
7. Functions and their Properties
8. Functions and their Graphs
9. Trigonometric Functions
10. Limits and the Notion of Continuity
11. Continuous Functions
12. Some Consequences of Continuity
13. Best Affine Approximations
14. Derivatives, and Rates of Change
15. Differentiation of Polynomials and Rational Functions
16. Differentiation of Compositions of Functions
What You Will Learn in Difference Equations to Differential Equations
"Difference Equations to Differential Equations: An introduction to calculus" by Dan Sloughter offers a fresh, intuitive path into "calculus" by first introducing students to "difference equations"—discrete versions of change over time. Rather than jumping straight into derivatives and integrals, the book builds understanding through sequences, patterns, and basic functions. This makes it ideal for beginners who want a smoother transition into more advanced calculus topics.
The book gradually shifts focus from discrete to continuous models, helping readers connect the dots between "difference equations" and "differential equations". With clear explanations, graphs, and real-world examples, Sloughter guides learners through concepts like limits, derivatives, integrals, and even Taylor series. Each chapter includes problems that encourage active engagement and critical thinking, supporting both independent learning and classroom use.
This book is designed for undergraduate students and motivated learners, it stands out by emphasizing conceptual understanding over memorization. It bridges gaps between high school math and college-level "differential equations", making it a valuable resource for anyone seeking a deeper grasp of how mathematical change is modeled and understood.
Book Details & Specifications
Title:
Difference Equations to Differential Equations by Dan Sloughter
Publisher:
Dan Sloughter
Year:
2000
Pages:
599
Type:
PDF
Language:
English
ISBN-10 #:
1616100257
ISBN-13 #:
978-1616100254
License:
CC BY-ND 3.0
Amazon:
Amazon
About the Author: Dan Sloughter
The author
Dan Sloughter
is a professor of mathematics at Furman University with a passion for making advanced math accessible. He specializes in "mathematics education", focusing on helping students bridge the gap between foundational and theoretical concepts. His book, "Difference Equations to Differential Equations", reflects his commitment to "conceptual understanding" and "clear mathematical exposition". By linking discrete and continuous methods, Sloughter supports learners in developing a deeper, more intuitive grasp of calculus. His work continues to influence how math is taught in undergraduate programs.
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