# Calculus 1

Most of the following videos were created for an AP Calculus course using the 2015-2016 syllabus. Some topics are not covered in depth but are more of a surface understanding. Some Calculus topics are not included.

**NOT ALL VIDEOS ARE CLOSED CAPTIONED but this process is being worked on.**

### Math 180 Spring 2019

**Make sure you watch the videos on Playposit.com to earn credit. These are here only if you want to rewatch them.**

**Infinite Limits and Vertical Asymptotes**

**Continuity**

**Limits at Infinity and Horizontal Asymptotes**

**Definition of Derivative at x=a**

**Power Rule and more**

**Product/Quotient Rule & Trig Derivatives**

**Chain Rule**

**Implicit Differentiation**

**Rates of Change**

**Related Rates**

**Linear Approximxations**

**Antiderivatives**

**Approximating Area**

**Fundamental Theorem of Calculus**

**u-substitution**

**Integration by parts**

**Net Change**

**Extreme Values**

**Analyzing Critical Values**

**Optimization**

**Sketching the Graph of f(x)**

**LHopital's Rule**

**IVT/MVT/Rolle's Theorem**

### 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)

**Related Rates (More Examples)**** **(≈47 min)7

### Integrals

**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)