Robert Gardner's Online Calculus 1 with Links to ETSU's Panopto Host

Online Calculus 1
with online videos Dr. Bob's Online University
(Not an actual university)
Robert 'Dr. Bob' Gardner

This website includes links to class notes and supplements (in PDF) used in the teaching of East Tennessee State University's Calculus 1 (MATH 1910). Links are also available for video presentations of the notes. The videos have been used as of the teaching of online Calculus 1, starting in fall 2020. The material is based closely on Joel Hass, Christopher Heil, and Maurice Weir's Thomas' Calculus: Early Transcendentals, 14th edition, Pearson (2018):

Thomas' Calculus: Early Transcendentals book, 14th edition

Robert "Dr. Bob" Gardner can be reached by e-mail at: gardnerr@etsu.edu. His office is in Gilbreath Hall, Room 308F on the ETSU campus.

Videos for these sections are online at the Online Calculus 1 Videos webpage.

Appendices.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
A.1. Real Numbers and the Real Line	A.1 Notes	A.1 Supplement A.1 Supplement Print File	Exercise A.1.15 Exercise A.1.21 Exercise A.1.29
A.2. Mathematical Induction	A.2 Notes	A.2 Supplement A.2 Supplement Print File	-
A.3. Lines Circles and Parabolas	-	-	-
A.4. Proofs of Limit Theorems	A.4 Notes	A.4 Supplement A.4 Supplement Print File	-
A.5. Commonly Occurring Limits	-	-	-
A.6. Theory of the Real Numbers	A.6 Notes	-	-

Chapter 1. Functions.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
1.1. Functions and Their Graphs	1.1 Notes	1.1 Supplement 1.1 Supplement Print File	Exercise 1.1.9 Exercise 1.1.21 Exercise 1.1.29(a)
1.2. Combining Functions; Shifting and Scaling Graphs	-	-	-
1.3. Trigonometric Functions	1.3 Notes	1.3 Supplement 1.3 Supplement Print File	Exercise 1.3.9 Exercise 1.3.29 Exercise 1.3.41 Exercise 1.3.57 Exercise 1.3.61 Exercise 1.3.65
1.4. Graphing with Software	-	-	-
1.5. Exponential Functions	1.5 Notes	1.5 Supplement 1.5 Supplement Print File	Exercise 1.5.9 Exercise 1.5.21 Exercise 1.5.29 Exercise 1.5.33
1.6. Inverse Functions and Logarithms	1.6 Notes	1.6 Supplement 1.6 Supplement Print File	Exercise 1.6.33 Exercise 1.6.53 Exercise 1.6.85 Exercise 1.6.87

Chapter 2. Limits and Continuity.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
2.1. Rates of Change and Tangent Lines to Curves	2.1 Notes	2.1 Supplement 2.1 Supplement Print File	Exercise 2.1.5 Exercise 2.1.11 Exercise 2.1.17
2.2. Limit of a Function and Limit Laws	2.2 Notes	2.2 Supplement 2.2 Supplement Print File	Exercise 2.2.25 Exercise 2.2.37 Exercise 2.2.65a
2.3. The Precise Definition of a Limit	2.3 Notes	2.3 Supplement 2.3 Supplement Print File	Exercise 2.3.13 Exercise 2.3.19 Exercise 2.3.25 Exercise 2.3.37 Exercise 2.3.41 Exercise 2.3.49
2.4. One-Sided Limits	2.4 Notes	2.4 Supplement 2.4 Supplement Print File	Exercise 2.4.9 Exercise 2.4.17 Exercise 2.4.19 Exercise 2.4.29 Exercise 2.4.33 Exercise 2.4.41 Exercise 2.4.45 Exercise 2.4.51 Exercise 2.4.53
2.5. Continuity	2.5 Notes	2.5 Supplement 2.5 Supplement Print File	Exercise 2.5.21 Exercise 2.5.33 Exercise 2.5.37 Exercise 2.5.57 Exercise 2.5.69
2.6. Limits Involving Infinity; Asymptotes of Graphs	2.6 Notes	2.6 Supplement 2.6 Supplement Print File	Exercise 2.6.17 Exercise 2.6.41 Exercise 2.6.65 Exercise 2.6.67 Exercise 2.6.73 Exercise 2.6.85 Exercise 2.6.89

Chapter 3. Derivatives.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
3.1. Tangent Lines and the Deriviative at a Point	3.1 Notes	3.1 Supplement 3.1 Supplement Print File	Exercise 3.1.9 Exercise 3.1.21 Exercise 3.1.25 Exercise 3.1.29 Exercise 3.1.37
3.2. The Derivative as a Function	3.2 Notes	3.2 Supplement 3.2 Supplement Print File	Exercise 3.2.5 Exercise 3.2.12 Exercise 3.2.17 Exercise 3.2.41 Exercise 3.2.57
3.3. Differentiation Rules	3.3 Notes	3.3 Supplement 3.3 Supplement Print File	Exercise 3.3.13 Exercise 3.3.25 Exercise 3.3.45 Exercise 3.3.57 Exercise 3.3.69
3.4. The Derivative as a Rate of Change	3.4 Notes	3.4 Supplement 3.4 Supplement Print File	Exercise 3.4.5
3.5. Derivatives of Trigonometric Functions	3.5 Notes	3.5 Supplement 3.5 Supplement Print File	Exercise 3.5.9 Exercise 3.5.12 Exercise 3.5.17 Exercise 3.5.30 Exercise 3.5.32 Exercise 3.5.49
3.6. The Chain Rule	3.6 Notes	3.6 Supplement 3.6 Supplement Print File	Exercise 3.6.33 Exercise 3.6.67 Exercise 3.6.69 Exercise 3.6.77 Exercise 3.6.89 Exercise 3.6.97 Exercise 3.6.99 Exercise 3.6.105
3.7. Implicit Differentiation	3.7 Notes	3.7 Supplement 3.7 Supplement Print File	Exercise 3.7.25 Exercise 3.7.41
3.8. Derivatives of Inverse Functions and Logarithms	3.8 Notes	3.8 Supplement 3.8 Supplement Print File	Exercise 3.8.33 Exercise 3.8.37 Exercise 3.8.41 Exercise 3.8.57
3.9. Inverse Trigonometric Functions	3.9 Notes	3.9 Supplement 3.9 Supplement Print File	Exercise 3.9.45
3.10. Related Rates	3.10 Notes	3.10 Supplement 3.10 Supplement Print File	Exercise 3.10.13 Exercise 3.10.25 Exercise 3.10.29 Exercise 3.10.31 Exercise 3.10.33 Exercise 3.10.41
3.11. Linearization and Differentials	3.11 Notes	3.11 Supplement 3.11 Supplement Print File	Exercise 3.11.5 Exercise 3.11.53

Chapter 4. Applications of Derivatives.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
4.1. Extreme Values of Functions on Closed Intervals	4.1 Notes	4.1 Supplement 4.1 Supplement Print File	Exercise 4.1.53 Exercise 4.1.59
4.2. The Mean Value Theorem	4.2 Notes	4.2 Supplement 4.2 Supplement Print File	Exercise 4.2.1 Exercise 4.2.5 Exercise 4.2.65 Exercise 4.2.73
4.3. Monotonic Functions and the First Derivative Test	4.3 Notes	4.3 Supplement 4.3 Supplement Print File	Exercise 4.3.23 Exercise 4.3.41 Exercise 4.3.45 Exercise 4.3.73
4.4. Concavity and Curve Sketching	4.4 Notes	4.4 Supplement 4.4 Supplement Print File	Exercise 4.4.19 Exercise 4.4.25 Exercise 4.4.41 Exercise 4.4.95 Exercise 4.4.97
4.5. Indeterminate Forms and L'Hopital's Rule	4.5 Notes	4.5 Supplement 4.5 Supplement Print File	Exercise 4.5.31 Exercise 4.5.39 Exercise 4.5.53 Exercise 4.5.61 Exercise 4.5.73
4.6. Applied Optimization	4.6 Notes	4.6 Supplement 4.6 Supplement Print File	Exercise 4.6.3 Exercise 4.6.9 Exercise 4.6.17 Exercise 4.6.25 Exercise 4.6.33 Exercise 4.6.37 Exercise 4.6.45 Exercise 4.6.49a Exercise 4.6.69
4.7. Newton's Method	4.7 Notes	4.7 Supplement 4.7 Supplement Print File	Exercise 4.7.1 Exercise 4.7.5
4.8. Antiderivatives	4.8 Notes	4.8 Supplement 4.8 Supplement Print File	Exercise 4.8.29 Exercise 4.8.41 Exercise 4.8.57 Exercise 4.8.97 Exercise 4.8.105

Chapter 5. Integrals.

SECTION	NOTES	SUPPLEMENTS	SOLUTIONS
5.1. Area and Estimating with Finite Sums	5.1 Notes	5.1 Supplement 5.1 Supplement Print File	Exercise 5.1.5 Exercise 5.1.9 Exercise 5.1.21
5.2. Sigma Notation and Limits of Finite Sums	5.2 Notes	5.2 Supplement 5.2 Supplement Print File	Exercise 5.2.27 Exercise 5.2.49
5.3. The Definite Integral	5.3 Notes	5.3 Supplement 5.3 Supplement Print File	Exercise 5.3.5 Exercise 5.3.67
5.4. The Fundamental Theorem of Calculus	5.4 Notes	5.4 Supplement 5.4 Supplement Print File	Exercise 5.4.36 Exercise 5.4.37 Exercise 5.4.45 Exercise 5.4.49 Exercise 5.4.53 Exercise 5.4.61
5.5. Indefinite Integrals and the Substitution Method	5.5 Notes	5.5 Supplement 5.5 Supplement Print File	Exercise 5.5.13 Exercise 5.5.37 Exercise 5.5.41 Exercise 5.5.45 Exercise 5.5.53 Exercise 5.5.57 Exercise 5.5.73
5.6. Definite Integral Substitutions and the Area Between Curves	5.6 Notes	5.6 Supplement 5.6 Supplement Print File	Exercise 5.6.33 Exercise 5.6.41 Exercise 5.6.57 Exercise 5.6.85 Exercise 5.6.89 Exercise 5.6.108

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Last updated: March 15, 2024.