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MAT 225 - Calculus I

Syllabus (Fall 2022)

Course Description: Calculus is the mathematical study of change that has widespread applications in science, engineering, economics and business. This course provides a rigorous introduction to singlevariable calculus. Topics include limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions, applications of derivatives, and integration, including the Fundamental Theorem of Calculus. This course will encourage students to think beyond memorizing formulas and to work towards understanding concepts.

Course Timeline and Notebooks

Below is a tentative timeline for our course. It includes preparatory work that should be done prior to each class meeting, a detailed set of notes corresponding to each class meeting, and assignments following each class meeting. Application and project topics may change due to students interests and/or developments in current events.

Meeting Number(s) Before Class Topic Assignments and Due Dates
1 Review Syllabus
3Blue1Brown: The Essence of Calculus
Algebra Foundations Review
Limits and their Properties  
2   One-Sided Limits  
3   Limits and Continuity  
4   Limits at Infinity  
5 Review Chapter 1 Group Exam I  
6 Review Chapter 1 and Group Exam Individual Exam I  
7 3Blue1Brown: The Paradox of the Derivative Instantaneous Rates of Change  
8 Foundations and Motivation for Derivatives The Derivative as a Function  
9 3Blue1Brown: Derivatives Through Geometry Derivative Rules  
10 3Blue1Brown: Visualizing the Chain and Product Rules The Chain Rule  
11 3Blue1Brown: Implicit Differentials, What’s Going On Here?
Chain Rule Version of Derivative Rules
Implicit Differentiation  
12 3Blue1Brown: What’s So Special about $e$?
Review Chapter 2
Group Exam II  
13 Review Chapter 2 and Group Exam Individual Exam II Watch for Recap: 3Blue1Brown: Limits and the Definition of Derivatives
14   Extreme Values  
15   The Mean Value Theorem  
16   Increasing and Decreasing Functions  
17   Concavity  
18   Related Rates  
19   Optimization  
20 Review Chapters 3 and 4 Group Exam III  
21 Review Chapters 3, 4, and Group Exam Individual Exam III  
22 3Blue1Brown: Integrals Antiderivatives and Indefinite Integrals  
23   Riemann Sums and The Definite Integral  
24 3Blue1Brown: What Does Area have to do with Slope? The Fundamental Theorem of Calculus  
25   Integration by Substitution  
26   Review  
27   Review  
28   Required: Final Exam Part A (Integration and Applications of Differentiation)  
29   Optional: Final Exam Part B (Limits and Derivative Rules)  



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