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Calculus I Lecture Notes:
Fall 2022
Daniel R. Jordan
Contents
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Contents
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Front Matter
1
Functions
Functions and Their Graphs
Combining Functions
Trigonometric Functions
Graphing with Software
Exponential Functions
Inverse Functions and Logarithms
2
Limits and Continuity
Rates of Change and Tangents to Curves
Limit of a Function and Limit Laws
The Precise Definition of a Limit
One-Sided Limits
Continuity
Limits Involving Infinity; Asymptotes of Graphs
3
Derivatives
Tangents and the Derivative at a Point
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Inverse Functions and Logarithms
Inverse Trigonometric Functions
Related Rates
Linearization and Differentials
4
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
L'Hospital's Rule
Applied Optimization
Newton's Method
Antiderivatives
5
Integration
Area and Estimating with Finite Sums
Sigma Notation and Limits of Finite Sums
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Substitution Method
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Section
4.7
Newton's Method
Note: skipping 4.7 on Newton's Method; included in Numerical Analysis.