# Calculus 1

The following videos on the left column were created for Math 180 at Mt. SAC. The videos in the last column were created for a high school AP Calculus course using the 2015-2016 syllabus. Some topics are not included and some are not in depth.

**If you are enrolled in a course at Mt. SAC, visit Playposit.com for captioned versions of required videos.**

### Math 180 Videos

*If you are currently enrolled in Math 180, make sure you watch the videos through Canvas on Playposit.com to earn credit*.

*If you are currently enrolled in Math 180, make sure you watch the videos through Canvas on Playposit.com to earn credit*.

**Infinite Limits and Vertical Asymptotes**

**Limits at Infinity and Horizontal Asymptotes**

**Definition of Derivative at x=a**

**Product and Quotient Rule & more**

**Areas and Distances, Integral as Riemann Sum**

**Definite Integral (Graphical Interpretation)**

**Fundamental Theorem of Calculus**

**Integrals involving transcendental functions**

### Math 180 Notes

*Below are copies of the written notes for the class. They are similar but not identical to the content in the video lessons.*

### AP Calculus AB videos

### Limits

**Limits: An Introduction**** **(≈46 min)

**Infinite Limits and Vertical Asymptotes** (≈29 min)

**Limits at Infinity and Horizontal Asymptotes** (≈32 min)

**Reading Limits from a graph**** **(≈12 min)

**Limit Laws** (≈16 min)

**Continuity**** **(≈32 min)

**Trigonometric Limits** (≈11 min)

**Evaluating Limits Algebraically** (≈39 min)

### Derivatives

**Defn of the derivative at x=a**** **(≈34 min)

**Derivative as a function**** **(≈18 min)

**Reading graph of f(x) to find derivatives **(≈44 min)

**Power Rule and Higher Derivatives** (≈48 min)

**Power Rule and Higher Derivatives** (25 min)

**Derivatives as Slopes of Tangent Lines** (≈17 min)

**Product and Quotient Rule** (≈30 min)

**Tangent Lines and Normal Lines**(≈22 min)

**Chain Rule**** **(≈30 min)

**AP Chain Rule **(≈49 min)

**Derivatives of Exponentials and Logs** (≈35 min)

**Derivatives of Inverse Functions** (≈13 min)

**Derivatives of Inverse Trig Functions**** **(≈15 min)

**Implicit Differentiation** (≈29 min)

**Linear Approximations** (≈24 min)

**L'Hopital's Rule** (≈22 min)

**Applications of Derivatives**

**Extreme Values** (≈32 min)

**Intro to Monotonicity **** **(≈41 min)

**Intro to Concavity ** (≈29 min)

**Analyzing Critical Values**** **(≈33 min)

**Interpreting the graph of f '(x) and f ''(x)** (≈24 min)

**Graph Sketching**(≈31 min)

**Intro to Rates** (≈50 min)

**Rates of Change (The Basics) **(≈58 min)

**Rates of Change (Examples)** (≈37 min)

**Intermediate Value Theorem, Mean Value Theorem, Rolle's **(≈23 min)

**Related Rates (The Basics)** (≈31min)

**Antiderivatives**** **(≈ 29 min)

**Differential Equations**** **(≈ 30 min)

**Areas and Distances**** **(≈29 min )

**Approximating Area:RAM**** **(≈62 min )

**Definite Integral**** **(≈61 min)

**Fundamental Theorem of Calculus (32 min)**

**FTC (Part 1)**** **(≈23 min)

**FTC (Part 2)**** **(≈45 min)

**AP RAM and TAM**** **** **(≈37 min)

**AP FTC**** **(≈55 min)

**Substitution Method (Indefinite Integrals)** (≈30 min)

**Substitution Method (Definite Integrals)** (≈17 min)

**Integrals involving Transcendental Functions** (≈9 min)

**Integration by Parts (≈ 27 min) **

**Partial Fraction Integration Basics** (≈35 min)

**Integral Test (for series)** (≈8 min)

**Methods of Integration**** **(≈43 min)

(includes basic integrals using substitution, integration by parts, basic partial fraction decomposition)

### Applications of Integration

**Integral as a Net change** (≈31 min)

**AP Net Change (part 1)** (≈55 min)

**AP Net Change (part 2)** (≈47 min)