BL

WB

William B

### Series Details

About

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.

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).

✋ 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

### About the Tutor

BL

WB

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

Lc

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

Dr

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

Df

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

Cd

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?

31

Aug

Af

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

Af

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?

5.9 - What’s important about:

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

Ic

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

Ic

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?

Add multiple expressions?

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

Ic

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

De

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

De

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

Ai

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

Ai

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

Pf

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

Is

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

Is

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?