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Calculus • Series

# Learn AP Calculus BC in 60 days!

Starts in 14 days!

William B

### Series Details

Covers all the contents from AP Calculus BC in the period of two months; please view the descriptions of each session to see what is covered.
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Online sessions are going to be fast paced, so it is important that you take notes. Expect to participate regularly, and give ideas when asked about a math problem you might not know how to answer. Because the AP Calculus Exams don’t require a full understanding of proofs of basic derivatives and integrals, I unfortunately won’t be covering them(though it may be a good idea to).
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✋ ATTENDANCE POLICY

Make as many of the session as you can; if you can't make one, you may have to review the materials independently and/or make up in office hours.

Dates

August 27 - September 12

Learners

10 / 50

Total Sessions

16

Yo, I'm a junior that's a chess and basketball enthusiast. I'm also a good source for single variable calculus or general chemistry. Currently studying several subjects: organic chemistry; calculus-based physics; differential equations; linear algebra; multivariable calculus; etc.

View William B's Profile

### Upcoming Sessions

16
27
Aug

Session 1

#### Limits and continuity

Structure of Sessions
1.1 - How do we find instantaneous rate of change?
1.2 - How is a limit different from the value of a function?
1.3 - Can you estimate a limit from a table of values?
1.4 - Can you determine limits graphically?
1.5 - What’s a one-sided limit?
1.6 - Can you determine limits using algebra?
1.7 - Can you figure out techniques of solving for limits?
1.8 - Can you find limits using the squeeze theorem?
1.9 - Can you select procedures for evaluating limits efficiently?
1.10 - What types of discontinuities can occur?
1.11 - What are the conditions for continuity?
1.12 - Can you justify continuity over an interval?
1.13 - What’s a removable discontinuity?
1.14 - How do we find limits at vertical asymptotes?
1.15 - How do we find limits at infinity?
28
Aug

Session 2

#### Differentiation: definition and basic derivative rules

2.1 - What’s the limit definition of a derivative?
2.2 - How do we solve the limit form of a derivative?
2.3 - How can we estimate derivatives?
2.4 - What’s the definition of differentiability?
2.5 - What’s the power rule?
2.6 - How do we differentiate a function with multiple components?
2.7 - What are the derivatives for sin(x), cos(x), ex, and ln(x)?
2.8 - What is the product rule?
2.9 - What is the quotient rule?
2.10 - What are the derivatives of all trig functions?
29
Aug

Session 3

#### Differentiation: composite, implicit, and inverse functions

3.1 - When is the chain rule applied?
3.2 - How can we implicitly derive equations with inseparable y and x terms?
3.3 - What is the definition of a derivative of an inverse function?
3.4 - What are the derivatives of all inverse trig functions?
3.5 - Can you select procedures for evaluating derivatives efficiently?
3.6 - How do we find 2nd, or 3rd order derivatives?
30
Aug

Session 4

#### Contextual applications of differentiation

4.1 and 4.3 - What does the derivative mean in context?
4.2 - What about in the context of physics?
4.4 and 4.5 - How can we solve related rates problems?
4.6 - How can we approximate values of a function using tangent lines?
4.7 - When is it appropriate to apply L’hospital’s rule?
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31
Aug

Session 5

#### Applying derivatives to analyze functions

5.1 - What is the MVT?
5.2 - What is the EVT?
5.3 - How can we use derivatives to determine intervals where a function is increasing/decreasing?
5.4 - How can we use the first derivative to find local maxes and mins?
5.5 - What’s different with the candidates test?
2
Sep

Session 6

#### Applying derivatives to analyze functions

5.6 - What is concavity? How can we determine concavity across an interval?
5.7 - How can we use a second derivative to find local maxes and mins?
5.8 - Can you sketch the relative graph of a function if given a derivative?
The first derivative?
The second derivative?
5.10 and 5.11 - How can we optimize a value in a certain situation?
5.12 - What’s a critical point?
3
Sep

Session 7

#### Integration and accumulation of change

6.1 - What do integrals mean in context?
6.2 - How can we approximate areas using different types of Riemann sums?
6.3 - How do we convert summation notation expressions into definite integrals?
4
Sep

Session 8

#### Integration and accumulation of change

6.4 - What is the FTC?
6.5 - How can we predict the behavior of an antiderivative from an equation?
6.6 - What happens if we do the following to an integral:
Switch the bounds?
Add a coefficient inside the integral?
6.7 - How can we evaluate the derivative of an integral with variable bounds?
6.8 - What is an indefinite integral?
6.9 - How can we solve integrals using u-substitution?
6.10 - How can we solve integrals using long division or completing the square?
5
Sep

Session 9

#### Integration and accumulation of change

(BC only) 6.11 - How can we solve integrals by reversing product rule?
(BC only) 6.12 - How can we solve integrals by decomposing a function into linear partial fractions?
(BC only) 6.13 - How can we evaluate integrals with improper bounds?
6
Sep

Session 10

#### Differential equations

7.1 - What is a differential equation?
7.2 - Can you verify a solution for a differential equation?
7.3 and 7.4 - Can you sketch/determine the slope field for a differential equation?
7.6 - How do we solve for a general solution to a separable differential equations?
7.7 - Can you find the particular solution from a general solution if given an initial condition?
7.8 - What is the structure and general solution to an exponential model?
7
Sep

Session 11

#### Differential equations

(BC only)7.5 - How do we approximate functions using Euler’s method?
(BC only)7.9 - What is the structure and general solution for a logistic model?
8
Sep

Session 12

#### Applications of integration

8.1 - How can you find the average value for a function across an interval?
8.2 - Can you apply integrals in a physics context?
8.3 - Can you apply the FTC(definite integrals) in various contexts?
8.4, 8.5, 8.6 - Can you find the area between two or more curves, whether they’re functions of x or y?
9
Sep

Session 13

#### Applications of integration

8.7 and 8.8 - Can you find the volume of solids with a cross section representing squares, rectangles, triangles, or semicircles?
8.9 and 8.10 - Can you find the volume of a solid with a rotating cross section using the disc method?
8.11 and 8.12 - Can you find the volume of a solid with a rotating cross section using the washer method?
(BC only) 8.13 - Can you find the arc length of a function?
10
Sep

Session 14

#### Parametric equations, polar coordinates, and vector-valued functions

9.1 and 9.2 - What is a parametric equation, and how can we solve for dy/dx?
9.3 - How do we find the arc length of a parametric equation?
9.4 and 9.5 - What are vector valued functions, and how do we differentiate and integrate them?
9.6 - How do we solve for the speed of a parametric across a point?
9.7 - What is a polar curve? How do we convert to cartesian coordinates to differentiate them?
9.8 and 9.9 - How do we find the area of a polar region bounded by one or multiple curves?
11
Sep

Session 15

#### Infinite sequences and series

10.1 - What is convergence versus divergence of an infinite series?
10.2 - When does a geometric series converge, and to what sum?
10.3 - What does the nth term test tell us?
10.4 - When do we use the integral test?
10.5 - When do we use the p-series test?
10.6 - When do we use the direct and limit comparison tests?
10.7 - When do we use the alternating series test?
10.8 - When do we use the ratio test?
10.9 - How do we determine absolute and conditional convergence of a series?
10.10 - What is the error bound for a partial sum of an alternating series?
12
Sep

Session 16

#### Infinite sequences and series

10.11 - What are Taylor polynomials?
10.12 - How can we determine the error bound for a taylor approximation of a function?
10.13 - How can we determine the interval of convergence for an infinite series with x, if we use the ratio test?
10.14 - How do we calculate the taylor series for a function?
10.15 - How do we integrate or differentiate functions represented as infinite series?