Calculus 1

Most of the following videos were created for an AP Calculus course using the syllabus for the 2015-2016 school year. 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.

Limits

Limits: An Introduction(≈46 min)

Solutions

Recommended Videos: V1, V2, V3

Limits at Infinity and Horizontal Asymptotes (≈32 min)

Solutions

Recommended Videos: V1

Reading Limits from a graph (≈12 min)

Worksheet

Solutions

Recommended Videos: V1

Limit Laws (≈16 min)

Solutions

Recommended Videos: V1

Continuity (≈38 min)

Solutions

Recommended Videos: V1

Trigonometric Limits (≈11 min)

Solutions

Recommended Videos: V1

Evaluating Limits Algebraically (≈39 min)

Solutions

Worksheet

Worksheet solutions

Recommended Videos: V1, V2, V3, V4


Derivatives

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

Solutions

Recommended Videos: V1, V2, V3, V4, V5

Derivative as a function (≈18 min)

Solutions

Recommended Videos: V1

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

Solutions

Recommended Videos: V1, V2, V3

Power Rule and Higher Derivatives (≈48 min)

Solutions

Recommended Videos: V1

Power Rule and Higher Derivatives (25 min)

Solutions

Derivatives as Slopes of Tangent Lines (≈17 min)

Solutions

Product and Quotient Rule (≈30 min)

Solutions

Recommended Videos: V1, V2

Tangent Lines and Normal Lines(≈22 min)

Solutions

Recommended Videos: V1

Chain Rule (≈30 min)

Solutions

Recommended Videos: V1, V2, V3

AP Chain Rule (≈49 min)

Solutions

Derivatives of Exponentials and Logs (≈35 min)

Solutions

Recommended Videos: V1

Derivatives of Inverse Functions (≈13 min)

Worksheet

Worksheet solutions

Derivatives of Inverse Trig Functions (≈15 min)

Solutions

Recommended Videos: V1, V2

Implicit Differentiation (≈29 min)

Solutions

AP worksheet solutions

Recommended Videos: V1, V2

Linear Approximations (≈24 min)

Worksheet

Solutions

Recommended Videos: V1

L'Hopital's Rule (≈22 min)

Solutions

AP worksheet solutions

Recommended Videos: V1 V2 V3 V4 V5 V6

Applications of Derivatives

Extreme Values (≈32 min)

Solutions

Recommended Videos: V1

Intro to Monotonicity (≈41 min)

Solutions

Intro to Concavity (≈29 min)

Solutions

Analyzing Critical Values (≈33 min)

Solutions

Solutions

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

Worksheet

Solutions

Graph Sketching(≈31 min)

Solutions

End of material for Test 5 Part 1

Intro to Rates (≈50 min)

Worksheet

Solutions

Recommended Videos: V1

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

Solutions 1

Solutions 2

Rates of Change (Examples) (≈37 min)

Worksheet

Worksheet solutions

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

Worksheet

Solutions

Related Rates (The Basics) (≈31min)

Solutions

Recommended Videos: V1, V2+

Related Rates (More Examples) (≈47 min)

Solutions

Worksheet

Worksheet Solutions

Recommended Videos: V1, V2, V3, V4, V5, V6, V7

Integrals

Antiderivatives (≈ 29 min)

Solutions

Differential Equations (≈ 30 min)

Book problems: p. 293 #47-67 odd, 71-75 all

Solutions

Areas and Distances (≈29 min )

Approximating Area:RAM (≈62 min )

Worksheet

Book problems: p. 308 #5,6,7,9,10

Book solutions

Worksheet Solutions

Definite Integral (≈61 min)

Solutions

Fundamental Theorem of Calculus (32 min)

FTC (Part 1) (≈23 min)

Solutions

FTC (Part 2) (≈45 min)

Solutions

AP RAM and TAM (≈37 min)

AP Worksheet

AP Worksheet solutions

AP FTC (≈55 min)

AP FTC Worksheet

Worksheet solutions

Substitution Method (Indefinite Integrals) (≈30 min)

Solutions

Recommended Videos: V1, V2, V3, V4, V5

Substitution Method (Definite Integrals) (≈17 min)

Solutions

Recommended Videos: V1, V2, V3, V4, V5

Integrals involving Transcendental Functions (≈9 min)

Solutions

Integration by Parts (≈ 27 min)

Solutions

Recommended Videos

Partial Fraction Integration Basics (≈35 min) [BC Topic]

Solutions

Integral Test (for series) (≈8 min) [BC Topic]

Assignment

Solutions

Recommended Videos: V1, V2

Methods of Integration (≈43 min)

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

BC Methods of Integration Worksheet

Solutions

Applications of Integration

Integral as a Net change (≈31 min)

Worksheet

Solutions

Recommended Videos: V1, V2, V3, V4, V5

AP Net Change (part 1) (≈55 min)

AP Net Change (part 2) (≈47 min)

AP packet

Solutions