Calculus Videos

Videos - Calculus 1

Most of these videos were recorded during the Fall of 2020, so if there is information given that you're not sure of, please ask me.

Included for a short time: Solutions to Exam 1

Week 1 videos

Week 2 Videos:
- Webwork video
- Quadratic inequalities
Overview of Trigonometry
- Trig review sheet. I've annotated the PDF to show which parts are most important.
- Video 1: Review of triangle trig
- Video 2: Review of circular trig and examples
- Video 3: Review of trig- Functions and examples
- OPTIONAL: Prof. Leonard overview (1.5 hours)
Practice with Limits (Section 2.3 with examples)
- Math 125, Section 2.3 (1 of 4)
- Math 125, Section 2.3 (2 of 4)
- Math 125, Section 2.3 (3 of 4)
- Math 125, Section 2.3 (4 of 4)
Section 2.5, Continuity.
- Video 1: Definition of Continuity, some theory
- Video 2: Examples using continuity
- Video 3: More examples using continuity
- Video 4: The Intermediate Value Theorem (IVT)
Section 2.6 (Limits at infinity, Horizontal Asymptotes)
- Extra Video Section 2.5: An extra couple of examples of continuity
- Video 1: Section 2.6, Limits at Infinity, Part 1 of 3
- Video 2: Section 2.6, Limits at Infinity, Part 2 of 3
- Video 3: Section 2.6, Limits at Infinity, Part 3 of 3
Section 2.7 (The Derivative as Number)
- Video 1: Section 2.7, Derivative as number, Part 1 of 2
- Video 2: Section 2.7, Derivative as number, Part 2 of 2
Section 2.8, The Derivative.
- Video 1: Section 2.8, Derivative as function, Part 1 of 4
- Video 2: Section 2.8, Derivative as function, Part 2 of 4
- Video 3: Section 2.8, Derivative as function, Part 3 of 4
- Video 4: Section 2.8, Derivative as function, Part 4 of 4
Section 3.1: Polynomials and Exponentials
- Section 3.1 Video 1 of 4
- Section 3.1 Video 2 of 4
- Homework from 3.1: Video 3 of 4A
- Homework from 3.1: Video 4 fo 4
Section 3.2 (The product and quotient rules)
- Video drill practice for Section 3.1 (to help you memorize the formulas)
- Section 3.2 Video 1 of 3- The product rule and quotient rule.
- Section 3.2 Video 2 of 3- Examples using the product and quotient rule
- Video drill practice for Section 3.2 (Video 3 of 3).
Section 3.3, Derivatives of trigonometric functions.
- Section 3.3 Video 0: Proof of Two Limits
- Section 3.3 Video 1: Trig Derivatives
- Section 3.3 Video 2: Sample exercises
Section 3.4, The Chain Rule
- Section 3.4, The Chain Rule (Video 1 of 3)
- Section 3.4, The Chain Rule (Video 2 of 3)
- Section 3.4, Examples (Video 3 of 3).
Section 3.5 Implicit Differentiation and Inverse Trig formulas.
- Overview, graphs and examples. Video 1 of 3
- More examples and notation. Video 2 of 3
- Relationships with inverses and inverse trig functions
Section 3.6 Logarithmic Differentiation.
- Video 1, Section 3.6 (Log diff)
- Video 2, Section 3.6 (Log diff).
Section 3.9 Related Rates
- Section 3.9 (Related Rates, or "Story Problems"). Background and setup
- Section 3.9, Example 1 (Planes to an airport)
- Section 3.9, Example 2 (Sand falling into a conical pile)
- Section 3.9, Example 3 (Balloon ascending)
- Section 3.9, Example 4 (Lamppost and Shadows)
- Section 3.9, Example 5 (Rocket ascending; height function given)
Section 3.10 (Linear approximations and differentials)
- Video 1: Linear approximations
- Video 2: Differentials
- Video 3: Examples.
Section 4.1 (Extrema, EVT, Closed Interval Method)
- Video 1: Introduction to Max/Min
- Video 2: Finish up intro (sorry for the video cutting abruptly!)
- Video 3: Examples
- Video 4: Fermat's Theorem and more examples
Section 4.2 (The MVT)
- Section 4.2: The Mean Value Theorem (Part 1)
- Section 4.2, Part 2
- Section 4.2, Part 3
Section 4.3 (Derivatives and the Shape of the Graph- Inc/Dec, CU/CD, etc)
- Section 4.3, Video 1
- Section 4.3, Video 2
- Section 4.3, a couple of examples
Section 4.4 (l'Hospital's rule)
- l'Hospital's rule. A bit about l'Hospital and setting the rule.
- Basic examples and indeterminant forms. Conversions to the basic form.
- More indeterminant forms and more algebra.
- Special examples to keep in mind...
Section 4.7 (Story problems - Optimization)
- Optimization intro, with examples
- Examples of optimization.
- More examples of optimization
- Even more examples of optimization!
- Hardcopy of the examples with solutions (in PDF form)
Section 4.9 (Antiderivatives)
- Antiderivatives, Part 1 (About 12 min)
- Antiderivatives, Part 2 (About 11 min)
- Antiderivatives, Part 3 (About 9 min)
- Graphical Antiderivatives, Part 4 (About 8 min)
NOTE: Fall '20, we did more than we're doing this semester (mostly due to the amount of review we did at the beginning of the semester). This semester, we did not go through Appendix E, and we had a streamlined section 5.2.
Appendix E (Sums and Sigma notation).
- Appendix E- Intro to Sigma Notation
- Definitions, formulas, and "Proof by Induction"
- Examples
5.1: Area and Distance
- Area and Distance- Part 1
- Part 2
- Part 3
5.2- The Definite Integral
- Video 1 of 3
- Video 2 of 3
- Video 3 of 3
5.3 - We will be discussing this on Friday (Dec 3)
- Section 5.3, Fundamental Theorem of Calculus Video 1
- FTC, video 2
- FTC, video 3
- FTC examples, video 4