Calculus for Everyone

This unique course is a truly classical approach to Calculus meaning that it is an integrated course that encompasses the physics and philosophy of motion as well as its mathematical description. Working through Calculus for Everyone: Understanding the Mathematics of Change by Mitch Stokes, we begin with the problem of change (motion) and walk through the major concepts in a typical Calculus I course (minus the transcendental functions) by examining the history of its development and its significance to/as natural philosophy. Class will consist of a combination of lectures, exercises, quizzes, and exams emphasizing both the history of the development of calculus and the mathematical knowledge of limits, derivatives, and integrals.

Importantly, all course content is normed to the Holy Scriptures by a teacher who acknowledges the historicity of the Genesis account as does the Lord Himself (Matt. 24: 37-39; Mark 10:6; Luke 3:38, 11:50-1, 17:26-7) and his apostles (Acts 17:24-7; Rom. 1:18-20, 5:12, 8:19-20; I Cor. 15: 21-2; 1 Pet. 3:20; 2 Pet. 2:5, 3:3-6), albeit implicitly. That is, Genesis chapter one is God’s own account (penned by Moses) of His Creation Ex Nihilo in six natural days some 6000 years ago (Gen. 5, 11; Luke 3) and Genesis chapters 6-9 describe a catastrophic global flood that profoundly impacted the earth's geology and in which all land animals and mankind perished save those on the ark.

This class meets for 32 weeks total divided into four eight-week quarters. Students will meet once a week for 90 minutes. Class will consist of lecture and subsequent recitation, and a weekly quiz after class due by Day's End. Each quarter students will be assigned weekly homework (reading, study questions, exercises). Each quarter will culminate with an exam covering that quarter's material with the exception of the final quarter which culminates with a comprehensive final exam.

Course Prerequisite and Sequencing:

Successfully completing Algebra I is the only prerequisite to/for taking this course.

Calculus for Everyone may be taken before, after, or alongside Geometry but should not be taken at its expense. It is not a substitute for PreCalculus (Trigonometry) nor is it equivalent to AP/college Calculus. Rather, by avoiding the "mire" of transcendental functions, it provides foundational skills in science processing earlier in high school, this being extremely valuable whether the student takes AP/college Calculus later, or not. This course is designed for students/parents who:

• Are seeking a classical approach to Calculus
• Value an historical approach that integrates mathematics with natural philosophy
• Want to understand how Calculus applies to the physical world
• Are STEM minded, or Liberal Arts minded, or both!

Course Objectives:

Throughout the course, students will learn:

1. About the need for Calculus and its historical development
2. To work with algebraic functions and their applications to problems
3. The concept of the derivative and what underlies it
4. To calculate derivatives for various functions using its definition vs. rules
5. To use differentiation to completely analyze the graph of a function
6. About various applications of the derivative
7. About the anti-derivative and the Fundamental Theorem of Calculus
8. To use integration to evaluate geometric areas and solve other applied problems

Texts:

• Calculus for Everyone: Understanding the Mathematics of Change by Mitch Stokes