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 for captioned versions of required videos.

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.

Limits Notes Key

Derivative Notes Key

Derivative Applications Notes Key

Integrals Notes Key

Analyzing Derivatives Notes Key

AP Calculus AB videos


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)


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)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)