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.


The following notes and supplements are all in PDF. The videos can be streamed from YouTube and should remain permanently available. (The videos previously on ETSU's Panopto host site have been, or may soon be, deleted.) Solutions to some exercises from the text book are online at the Online Calculus 1 Solutions to Various Exercises webpage.


Appendices.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
A.1. Real Numbers and the Real Line
A.1 Notes
A.1 Supplement
A.1 Supplement Print File
A.1 Video (1:03:29)
A.2. Mathematical Induction
A.2 Notes
A.2 Supplement
A.2 Supplement Print File
A.2 Video (51:08)
A.3. Lines Circles and Parabolas
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-
-
A.4. Proofs of Limit Theorems
A.4 Notes
A.4 Supplement
A.4 Supplement Print File
A.4 Video (41:40)
A.5. Commonly Occurring Limits
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-
-
A.6. Theory of the Real Numbers
A.6 Notes
-
A.6 Video (31:05)

Chapter 1. Functions.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
1.1. Functions and Their Graphs
1.1 Notes
1.1 Supplement
1.1 Supplement Print File
1.1 Video, Part 1 (18:27)
1.1 Video, Part 2 (59:57)
1.2. Combining Functions; Shifting and Scaling Graphs
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-
-
1.3. Trigonometric Functions
1.3 Notes
1.3 Supplement
1.3 Supplement Print File
1.3 Video (1:22:43)
1.4. Graphing with Software
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-
-
1.5. Exponential Functions
1.5 Notes
1.5 Supplement
1.5 Supplement Print File
1.5 Video (32:06)
1.6. Inverse Functions and Logarithms
1.6 Notes
1.6 Supplement
1.6 Supplement Print File
1.6 Video, Part 1 (38:17)
1.6 Video, Part 2 (43:36)


Chapter 2. Limits and Continuity.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
2.1. Rates of Change and Tangent Lines to Curves
2.1 Notes
2.1 Supplement
2.1 Supplement Print File
2.1 Video (1:22:07)
2.2. Limit of a Function and Limit Laws
2.2 Notes
2.2 Supplement
2.2 Supplement Print File
2.2 Video, Part 1 (58:54)
2.2 Video, Part 2 (52:58)
2.3. The Precise Definition of a Limit
2.3 Notes
2.3 Supplement
2.3 Supplement Print File
2.3 Video, Part 1 (1:02:31)
2.3 Video, Part 2 (1:05:06)
2.4. One-Sided Limits
2.4 Notes
2.4 Supplement
2.4 Supplement Print File
2.4 Video (1:33:40)
2.5. Continuity
2.5 Notes
2.5 Supplement
2.5 Supplement Print File
2.5 Video, Part 1 (57:52)
2.5 Video, Part 2 (54:01)
2.6. Limits Involving Infinity; Asymptotes of Graphs
2.6 Notes
2.6 Supplement
2.6 Supplement Print File
2.6 Video, Part 1 (1:34:08)
2.6 Video, Part 2 (1:32:44)


Chapter 3. Derivatives.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
3.1. Tangent Lines and the Deriviative at a Point
3.1 Notes
3.1 Supplement
3.1 Supplement Print File
3.1 Video (44:49)
3.2. The Derivative as a Function
3.2 Notes
3.2 Supplement
3.2 Supplement Print File
3.2 Video (1:08:02)
3.3. Differentiation Rules
3.3 Notes
3.3 Supplement
3.3 Supplement Print File
3.3 Video, Part 1 (27:30)
3.3 Video, Part 2 (28:09)
3.3 Video, Part 3 (42:02)
3.3 Video, Part 4 (36:47)
3.4. The Derivative as a Rate of Change
3.4 Notes
3.4 Supplement
3.4 Supplement Print File
3.4 Video, Part 1 (27:17)
3.4 Video, Part 2 (54:40)
3.5. Derivatives of Trigonometric Functions
3.5 Notes
3.5 Supplement
3.5 Supplement Print File
3.5 Video (39:09)
3.6. The Chain Rule
3.6 Notes
3.6 Supplement
3.6 Supplement Print File
3.6 Video (1:05:51)
3.7. Implicit Differentiation
3.7 Notes
3.7 Supplement
3.7 Supplement Print File
3.7 Video, Part 1 (45:31)
3.7 Video, Part 2 (39:14)
3.8. Derivatives of Inverse Functions and Logarithms
3.8 Notes
3.8 Supplement
3.8 Supplement Print File
3.8 Video (1:34:58)
3.9. Inverse Trigonometric Functions
3.9 Notes
3.9 Supplement
3.9 Supplement Print File
3.9 Video (1:08:37)
3.10. Related Rates
3.10 Notes
3.10 Supplement
3.10 Supplement Print File
3.10 Video (1:51:20)
3.11. Linearization and Differentials
3.11 Notes
3.11 Supplement
3.11 Supplement Print File
3.11 Video (1:06:02))

Chapter 4. Applications of Derivatives.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
4.1. Extreme Values of Functions on Closed Intervals
4.1 Notes
4.1 Supplement
4.1 Supplement Print File
4.1 Video (1:14:20)
4.2. The Mean Value Theorem
4.2 Notes
4.2 Supplement
4.2 Supplement Print File
4.2 Video* (1:10:53)
4.3. Monotonic Functions and the First Derivative Test
4.3 Notes
4.3 Supplement
4.3 Supplement Print File
4.3 Video (1:23:14)
4.4. Concavity and Curve Sketching
4.4 Notes
4.4 Supplement
4.4 Supplement Print File
4.4 Video (1:43:59)
4.5. Indeterminate Forms and L'Hopital's Rule
4.5 Notes
4.5 Supplement
4.5 Supplement Print File
4.5 Video** (1:28:11)
4.6. Applied Optimization
4.6 Notes
4.6 Supplement
4.6 Supplement Print File
4.6 Video, Part 1 (50:34)
4.6 Video, Part 2 (1:15:02)
4.7. Newton's Method
4.7 Notes
4.7 Supplement
4.7 Supplement Print File
4.7 Video, Part 1 (29:56)
4.7 Video, Part 2 (28:46)
4.8. Antiderivatives
4.8 Notes
4.8 Supplement
4.8 Supplement Print File
4.8 Video (1:18:48)
*A computational error appears in Exercise 4.2.40 in the video, which is corrected in the notes.
**A special case of l'Hopital's Rule (Theorem 4.6) is given in the video; it is corrected to the general form in the notes.


Chapter 5. Integrals.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
5.1. Area and Estimating with Finite Sums
5.1 Notes
5.1 Supplement
5.1 Supplement Print File
5.1 Video (1:11:57)
5.2. Sigma Notation and Limits of Finite Sums
5.2 Notes
5.2 Supplement
5.2 Supplement Print File
5.2 Video (1:05:55)
5.3. The Definite Integral
5.3 Notes
5.3 Supplement
5.3 Supplement Print File
5.3 Video, Part 1 (57:29)
5.3 Video, Part 2 (38:50)
5.4. The Fundamental Theorem of Calculus
5.4 Notes
5.4 Supplement
5.4 Supplement Print File
5.4 Video (1:10:28)
5.5. Indefinite Integrals and the Substitution Method
5.5 Notes
5.5 Supplement
5.5 Supplement Print File
5.5 Video (1:12:40)
5.6. Definite Integral Substitutions and the Area Between Curves
5.6 Notes
5.6 Supplement
5.6 Supplement Print File
5.6 Video (1:20:57)

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Last updated: March 14, 2024.