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Notes for Introductory Calculus (Math 120)
Brenton LeMesurier
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Front Matter
Copyright Page
Introduction
1
Functions and Graphs
1.1
Exponential Functions
1.1
References
1.1
Exercises
1.2
Inverse Functions
1.2
References
1.2
Exercises
1.3
Logarithmic Functions
1.3
References
1.3
Exercises
2
Limits
2.1
A Preview of Calculus
2.1
Exercises
2.2
The Limit of a Function
2.2
Exercises
2.3
The Limit Laws
2.3
Exercises
2.4
Continuity
2.4
Exercises
2.5
The Precise Definition of a Limit
2.5
Exercises
3
Derivatives
3.1
Defining the Derivative
3.1
Exercises
3.2
The Derivative as a Function
3.2
Exercises
3.3
Differentiation Rules
3.3
Exercises
3.4
Derivatives as Rates of Change
3.4
Exercises
3.5
Derivatives of Trigonometric Functions
3.5
Exercises
3.6
The Chain Rule
3.6
Exercises
3.7
Derivatives of Inverse Functions
3.7.1
A procedure using just the Chain Rule
3.7.2
The Power Rule
\((x^r)' = r x^{r-1}\)
for any rational number
\(r\)
3.7.3
Derivative of the Natural Logarithm
3.7.4
Verification of the Power Rule for all Real Powers
3.7.5
Derivatives of the Inverse Trigonometric Functions
3.7.5
Exercises
3.8
Implicit Differentiation
3.8
Exercises
3.9
Derivatives of Exponential and Logarithmic Functions (and
Logarithmic Differentiation
)
3.9
Exercises
4
Applications of Differentiation
4.1
Related Rates
4.1
Exercises
4.2
Linear Approximations and Differentials
4.2
Exercises
4.3
Maxima and Minima
4.3
Exercises
4.4
The Mean Value Theorem
4.4
Exercises
4.5
Derivatives and the Shape of a Graph
4.5
Exercises
4.6
Limits at Infinity and Asymptotes
4.6
Exercises
4.7
Applied Optimization Problems
4.7
Exercises
4.8
L’Hôpital’s Rule
4.8
Exercises
4.9
Newton’s Method (Omitted)
4.9
Exercises
4.10
Antiderivatives
4.10
Exercises
5
Integrals
5.1
Approximating Areas (and Distance Traveled)
5.1
Exercises
5.2
The Definite Integral
5.2
Exercises
5.3
The Fundamental Theorem of Calculus
5.3
Exercises
5.4
Integration Formulas and the Net Change Theorem
5.4
Exercises
5.5
Substitution
5.5
Exercises
5.6
Integrals Involving Exponential and Logarithmic Functions — Summary
5.6
Exercises
5.7
Integrals Resulting in Inverse Trigonometric Functions — Summary
5.7
Exercises
Appendices
A
Study Guide
B
Some Tables
Notes for Introductory Calculus (Math 120)
Brenton LeMesurier
Department of Mathematics
College of Charleston
Charleston, South Carolina
lemesurierb@cofc.edu
Last revised December 19, 2023 at 11:43:05 (-07:00)
Copyright Page
Introduction
