Calculus I Class Notes


I will pass these out in class and we will fill them out together. If you miss class or have insufficient notes, use the completed versions. I would not suggest you just print those; you should copy the material over to your own copy to help cement the ideas.

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 (Typos have since been fixed.)
3.3
 Rules of Differentiation Rules of Differentiation (Number 1e was changed for variety. Page 4 has notation detail added.)
3.4
 The Product and Quotient Rules The Product and Quotient Rules (Number 2 has since been spread out.)
3.5
 Derivatives of Trigonometric Functions Derivatives of Trigonometric Functions
3.6
 Derivatives as Rates of Change Derivatives as Rates of Change (Typos have since been fixed, spacing changed, and a question has been added.)
3.7
 The Chain Rule The Chain Rule (Typos have since been fixed and questions have been changed and added.)
3.8
 Implicit Differentiation Implicit Differentiation (I have since added detail to instructions for number 6.)
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