Calculus I Class Notes

I have many Class Notes written and some will be coming as we proceed. We will fill them out together as a class. I have posted hand-written notes from Spring 2025 that are the precursors of these.

Section

Name of Section

Book: Calculus: Early Transcendentals, 3rd edition, digital version, Briggs et al.

Completed Notes from Fall 2025

2.1
 The Idea of Limits The Idea of Limits

2.2

Definitions of Limits Definitions of Limits (Typos have since been fixed.)
2.3
 Techniques for Computing Limits Techniques for Computing Limits
2.4
 Infinite Limits Infinite Limits
2.5
 Limits at Infinity Limits at Infinity
2.6
 Continuity Continuity (Typos have since been fixed.)
3.1
 Introducing the Derivative Introducing the Derivative (Page 4 thought bubble has since been amended.)
3.2
 The Derivative as a Function The Derivative as a Function
3.3
 Rules of Differentiation Rules of Differentiation
3.4
 The Product and Quotient Rules The Product and Quotient Rules
3.5
 Derivatives of Trigonometric Functions Derivatives of Trigonometric Functions
3.6
 Derivatives as Rates of Change Derivatives as Rates of Change
3.7
 The Chain Rule The Chain Rule
3.8
 Implicit Differentiation Implicit Differentiation
3.9
 Related Rates Related Rates
4.1
 Maxima and Minima Maxima and Minima
4.2
 Mean Value Theorem Mean Value Theorem
4.3
 The First and Second Derivative Tests What Derivatives Tell Us (First and Second Derivative Tests)
4.4
 Putting it Together to Graph Functions Graphing Functions by Hand
4.5
 Optimization Problems Optimization Problems
4.6
 Linear Approximation and Differentials Linear Approximation and Differentials
4.7
 L'Hôpital's Rule

L'Hôpital's Rule

Additional Annotated Examples
4.8
 Newton's Method Newton's Method
4.9
 Antiderivatives Antiderivatives
5.1
 Riemann Sums: Approximating Areas Under Curves Riemann Sums: Approximating Areas Under Curves
5.2
 Riemann Sums: Definite Integrals Riemann Sums: Definite Integrals
5.3
 Fundamental Theorem of Calculus Fundamental Theorem of Calculus
5.4
 Working With Integrals: Even or Odd Functions and Average Values Working With Integrals: Even or Odd Functions and Average Values
5.5
 Integrals with u-Substitution Integrals with u-Substitution