Calculus videos

Introduction to Calculus (AP 1.1)

Introduction to limits

1. Definition of a limit and limit notation (AP 1.2)

2. Finding limits from graphs (AP 1.3)

3. Finding limits from tables (AP 1.4)

Limit properties also includes piecewise functions (AP 1.5)

Evaluating limits analytically 

1. Finding limits using algebra part 1 (AP 1.6) 

2. Finding limits using algebra part 2 includes radicals, complex fractions (AP 1.7)

Squeeze theorem (AP 1.8)

Continuity

1. Types of discontinuities (AP 1.10)

2. Definition of continuity (AP 1.11) 

3. Continuity over an interval includes discussion of endpoint continuity (AP 1.12)

4. Removable discontinuities (AP 1.13)

Intermediate Value Theorem (AP 1.16)

Infinite limits and limits at infinity

1. Infinite limits and vertical asymptotes (AP 1.14)

2. Limits at infinity and horizontal asymptotes (AP 1.15)

Instantaneous rate of change

1. Average vs instantaneous rate of change (AP 2.1, 2.3)

2. Definition of the derivative and derivative notation also includes writing tangent line equations (AP 2.2)

Differentiability (AP 2.4)

Derivative rules

1. Power rule (AP 2.5)

2. Properties of derivatives also includes horizontal tangent lines, normal lines, and piecewise functions (AP 2.6)

3. Derivatives of trigonometric and exponential/log functions (AP 2.7)

Product and quotient rules

1. Product rule (AP 2.8)

2. Quotient rule (AP 2.9)

3. But wait, there's more trig derivatives (AP 2.10)

Chain rule (AP 3.1)

Implicit differentiation

1. Implicit differentiation (AP 3.2)

2. Inverse trigonometric derivatives (AP 3.4)

3. Logarithmic differentiation 

Inverse differentiation (AP 3.3)

Review exercises

1. Lots of derivatives video 

Derivatives in context 

1. Derivatives in context part 1 (AP 4.1)

2. Derivatives in context part 2 (AP 4.3)

One-dimensional motion (AP 4.2)

Related rates

1. Related rates part 1 (AP 4.4)

2. Related rates part 2  (AP 4.5)

Linear approximation (AP 4.6)

L'Hospital's Rule (AP 4.7)

Critical points and extrema (AP 5.2)

Mean Value Theorem (AP 5.1)

Candidates test (AP 5.5)

First derivative test

1. Increasing and decreasing (AP 5.3)

2. First derivative test (AP 5.4)

Second derivative test

1. Concavity (AP 5.6)

2. Second derivative test (AP 5.7)

Curve sketching

1. Curve sketching part 1 (AP 5.8)

2. Curve sketching part 2

Optimization

1. Optimization part 1 (AP 5.10)

2. Optimization part 2 (AP 5.11)

Accumulation (AP 6.1)

Riemann sums (AP 6.2) 

Definite integrals includes summation (sigma) notation (AP 6.3)

Accumulation functions

1. Fundamental theorem of calculus (AP 6.4)

2. Practice with accumulation functions (AP 6.5)

Properties of definite integrals

1. Properties of definite integrals (AP 6.6)

2. Average value theorem (AP 8.1)

Antiderivatives

1. Fundamental theorem of calculus (again) (AP 6.7)

2. Antiderivative rules (AP 6.8)

Integration by substitution (u-sub)

1. U-sub (AP 6.9) 

2. Integration using long division and completing the square (AP 6.10)

Accumulation in context

1. One-dimensional motion with integrals (AP 8.2)

2. Accumulation in other contexts (AP 8.3)

Differential equations and slope fields

1. Modeling with differential equations (AP 7.1) 

2. Slope fields part 1 (AP 7.3)

3. Slope fields part 2  (AP 7.4)

Solving differential equations

1. General solutions (AP 7.6)

2. Particular solutions (AP 7.7)

Exponential equations (AP 7.8)

Area between curves

1. Area between curves with respect to x (AP 8.4)

2. Area between curves with respect to y (AP 8.5)

3. Area between curves with multiple intersection points (AP 8.6)

Volumes with cross sections

1. Square and rectangle cross sections (AP 8.7)

2. Triangle and semicircle cross sections (AP 8.8)

Volumes of solids of revolution

1. Disc method

   1. Disc method part 1 (AP 8.9)

   2. Disc method part 2 (AP 8.10)

2. Washer method

   1. Washer method part 1 (AP 8.11)

   2. Washer method part 2 (AP 8.12)

Integration by parts (AP 6.11)

Integration with partial fractions (AP 6.12)

Improper integrals (AP 6.13)

Trig integrals

1. U-sub with trigonometric functions

2. Trigonometric substitution

Arc length and surface area

1. Arc length (AP 8.13)

2. Surface area

Differential equations (again)

1. Euler's Method (AP 7.5)

2. Logistic equation (AP 7.9)

Parametric equations

1. Defining and differentiating parametric equations (AP 9.1)

2. Second derivatives of parametric equations (AP 9.2)

3. Arc length of parametric equations (AP 9.3)

Vector-valued functions

1. Defining and differentiating vector-valued functions (AP 9.4)

2. Integrating vector-valued functions (AP 9.5)

Motion with parametric and vector-valued functions (AP 9.6)

Polar coordinates

1. Defining and differentiating polar equations (AP 9.7)

2. Integrating polar equations (AP 9.8)

3. Area between polar curves (AP 9.9)

Unit 9A: Infinite series

1. Introduction to infinite series

   1. Convergent and divergent series (AP 10.1)

   2. Geometric series  (AP 10.2)

2. Tests for convergence/divergence

   1. nth term and integral tests

      1. nth term test (AP 10.3)

      2. Integral test (AP 10.4)

   2. Harmonic and p-series (AP 10.5)

   3. Comparison test and alternating series

      1. Comparison test (AP 10.6)

      2. Alternating series test (AP 10.7)

   4. Root and ratio test 

      1. Ratio test (AP 10.8)

      2. Root test

3. Absolute vs. conditional convergence (AP 10.9)

Unit 9B: Taylor and McLaurin series

1. Taylor polynomials (AP 10.11)

2. Lagrange error bound (AP 10.12)

3. Finding Taylor/McLaurin series for a function (AP 10.14)

4. Power series

   1. Radius and interval of convergence of power series (AP 10.13)

   2. Representing functions as power series (AP 10.15)