Calculus • Series
Get a 5! - AP Calculus BC/Calc II in a Month
PL
JG
Jose Roberto Cossich G
This series ended on August 12, 2024. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
I got a 5 on the AP Calculus BC exam, and you can too.
Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2, including a FULL work-through of a real past exam.
The first two sessions will serve as a review of differential calculus. Below are what we will cover:
INTEGRATION AND APPLICATIONS (UNIT 1)
1. Introduction to accumulation of change
2. Left and right Riemann sums; over and under-approximation
3. Midpoint and trapezoidal sums
4. Definition of indefinite integral using as the limit of Riemann sums
5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals
6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation.
7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds.
8. The reverse power rule, u-substitution, and integration by parts
9. Antiderivatives of all the previously mentioned functions
10. Improper integrals
11. Finding the average value of a function on an interval
12. Connecting position, velocity, and acceleration functions using integrals
13. Using accumulation functions and definite integrals in applied contexts
14. Finding the area between curves expressed as functions of x
15. Finding the area between curves expressed as functions of y
16. Finding the area between curves that intersect at more than two points
17. Volumes with cross sections: squares and rectangles
18. Volumes with cross sections: triangles and semicircles
19. Volume with disc method: revolving around x- or y-axis
20. Volume with disc method: revolving around other axes
21. Volume with washer method: revolving around x- or y-axis
22. Volume with washer method: revolving around other axes
23. The arc length of a smooth, planar curve and distance traveled
24. Calculator-active practice
DIFFERENTIAL EQUATIONS (UNIT 2):
1. Modeling situations with differential equations
2. Verifying solutions for differential equations
3. Sketching slope fields
4. Reasoning using slope fields
5. Approximating solutions using Euler’s method
6. Finding general solutions using separation of variables
7. Finding particular solutions using initial conditions and separation of variables
8. Exponential models with differential equations
9. Logistic models with differential equations
PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3):
1. Defining and differentiating parametric equations
2. Second derivatives of parametric equations
3. Finding arc lengths of curves given by parametric equations
4. Defining and differentiating vector-valued functions
5. Solving motion problems using parametric and vector-valued functions
6. Defining polar coordinates and differentiating in polar form
7. Finding the area of a polar region or the area bounded by a single polar curve
8. Finding the area of the region bounded by two polar curves
9. Calculator-active practice
INFINITE SERIES (UNIT 4):
1. Defining convergent and divergent infinite series
2. Working with geometric series
3. The nth-term test for divergence
4. Integral test for convergence
5. Harmonic series and p-series
6. Comparison tests for convergence
7. Alternating series test for convergence
8. Ratio test for convergence
9. Determining absolute or conditional convergence
10. Alternating series error bound
11. Finding Taylor polynomial approximations of functions
12. Lagrange error bound
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
✋ ATTENDANCE POLICY
I try to make the session times as accommodating as possible, however make-up sessions are always available. Please feel free to ask for one if needed!
Dates
July 13 - August 12
Learners
20 / 20
Total Sessions
26
About the Tutor
PL
JG
A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.
View Jose Roberto Cossich G's Profile
Upcoming Sessions
0
Past Sessions
26
13
Jul
OH
Session 1
Office Hours
REVIEW OF DIFFERENTIAL CALCULUS (PART 1) (75m)
1. Introduction to derivatives and notation
2. Average rate of change and the secant line
3. Instantaneous rate of change and the tangent line
4. The formal and informal definition of a derivative using limits
5. Equation of the tangent line of a function at a point
6. Estimating derivatives graphically and algebraically
7. Differentiability at a point and over an interval (connection to continuity)
8. Evaluating derivatives using the power rule, sum rule, product rule, quotient rule, and chain rule (including proofs of all the rules)
9. Derivative of sin(x), cos(x), tan(x), csc(x), sec(x), cot(x), ln(x), e^x, a^x, and log_a(x) (including a derivation of all of the formulas)
10. Derivative of inverse functions and inverse trigonometric functions
14
Jul
OH
Session 2
Office Hours
REVIEW OF DIFFERENTIAL CALCULUS (PART 2) (90m)
11. Second derivatives, implicit differentiation, and related rates
12. Position, velocity, and acceleration problems
13. Local linearity and linear approximations to functions
14. L'Hôpital's rule and the special case of L'Hôpital's rule
15. The Mean Value Theorem for derivatives, the Extreme Value Theorem, and Rolle's Theorem
16. Finding critical points, local minima and maxima, increasing and decreasing intervals of a function
17. Finding absolute extrema over closed intervals and over the entire domain of a function
18. Introduction to concavity
19. The Second Derivative Test and points of inflection
20. Optimization
15
Jul
Ic
Session 3
Integration and accumulation of change
Topics covered (75m):
1. Introduction to accumulation of change
2. Left and right Riemann sums; over and under-approximation
3. Midpoint and trapezoidal sums
16
Jul
Ic
Session 4
Integration and accumulation of change
Topics covered (80m):
4. Definition of indefinite integral using as the limit of Riemann sums
5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals
6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation.
7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds.
17
Jul
Ic
Session 5
Integration and accumulation of change
Topics covered (75m):
8. The reverse power rule, u-substitution, and integration by parts
9. Antiderivatives of all the previously mentioned functions
10. Improper integrals
18
Jul
OH
Session 6
Office Hours
Khan Academy Unit Test run-through (1h 20m)
Unit Test 6 "Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
19
Jul
Ai
Session 7
Applications of integration
(Continuing)
9. Integration by parts and
10. Improper integrals
20
Jul
Ai
Session 8
Applications of integration
Khan Academy Unit Test run-through (1h 20m)
Unit Test 6 "Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
21
Jul
Ai
Session 9
Applications of integration
Topics covered (75m):
11. Finding the average value of a function on an interval
12. Connecting position, velocity, and acceleration functions using integrals
13. Using accumulation functions and definite integrals in applied contexts
14. Finding the area between curves expressed as functions of x
22
Jul
Ai
Session 10
Applications of integration
Topics covered (75m):
15. Finding the area between curves expressed as functions of y
16. Finding the area between curves that intersect at more than two points
17. Volumes with cross sections: squares and rectangles
23
Jul
Ai
Session 11
Applications of integration
Topics covered (75m):
18. Volumes with cross sections: triangles and semicircles
19. Volume with disc method: revolving around x- or y-axis
20. Volume with disc method: revolving around other axes
PLEASE BRING YOUR GRAPHING CALCULATORS NEXT session!
(TI-84s preferred!)
24
Jul
Ai
Session 12
Applications of integration
PLEASE BRING YOUR GRAPHING CALCULATORS! (TI-84s preferred!)
Topics covered (80m):
21. Volume with washer method: revolving around x- or y-axis
22. Volume with washer method: revolving around other axes
23. The arc length of a smooth, planar curve and distance traveled
24. Calculator-active practice
26
Jul
OH
Session 13
Office Hours
Khan Academy Unit Test run-through (1h 20m)
"Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
27
Jul
De
Session 14
Differential equations
Topics covered (80m):
1. Modeling situations with differential equations
2. Verifying solutions for differential equations
3. Sketching slope fields
4. Reasoning using slope fields
5. Approximating solutions using Euler’s method
6. Finding general solutions using separation of variables
28
Jul
De
Session 15
Differential equations
Topics covered (80m):
7. Finding particular solutions using initial conditions and separation of variables
8. Exponential models with differential equations
9. Logistic models with differential equations
29
Jul
OH
Session 16
Office Hours
Khan Academy Unit Test run-through (1h 20m)
"Unit 8: Applications of integration"
*END OF UNIT 2 - DIFFERENTIAL EQUATIONS*
31
Jul
Pf
Session 17
Parametric equations, polar coordinates, and vector-valued functions
PLEASE BRING YOUR GRAPHING CALCULATORS NEXT SESSION!
(TI-84s preferred!)
Topics covered (80m):
1. Defining and differentiating parametric equations
2. Second derivatives of parametric equations
3. Finding arc lengths of curves given by parametric equations
1
Aug
Pf
Session 18
Parametric equations, polar coordinates, and vector-valued functions
Topics covered (80m):
4. Defining and differentiating vector-valued functions
5. Solving motion problems using parametric and vector-valued functions
6. Defining polar coordinates and differentiating in polar form
7. Finding the area of a polar region or the area bounded by a single polar curve
3
Aug
OT
Session 19
Other Topics
Topics covered (75m):
PLEASE BRING YOUR GRAPHING CALCULATORS! (TI-84s preferred!)
8. Finding the area of the region bounded by two polar curves
9. Calculator-active practice
*END OF UNIT 3 - PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS*
We'll start our next unit:
1. Defining convergent and divergent infinite series
4
Aug
OT
Session 20
Other Topics
Topics covered (75m):
2. Working with geometric series
3. The nth-term test for divergence
4. Integral test for convergence
6
Aug
OT
Session 21
Other Topics
Topics covered (75m):
5. Harmonic series and p-series
6. Comparison tests for convergence
7. Alternating series test for convergence
8. Ratio test for convergence
7
Aug
OT
Session 22
Other Topics
Topics covered (80m):
9. Determining absolute or conditional convergence
10. Alternating series error bound
11. Finding Taylor polynomial approximations of functions
9
Aug
OT
Session 23
Other Topics
Topics covered (80m):
12. Lagrange error bound
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
AC
Session 24
AP Calculus
Topics covered (80m):
11. Finding Taylor polynomial approximations of functions
12. Lagrange error bound
11
Aug
AC
Session 25
AP Calculus
Topics covered (80m):
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
12
Aug
AC
Session 26
AP Calculus
COURSE CHALLENGE (90m)
THE SERIES WILL END IN A WEEK; IN THAT TIME I WILL ACCEPT ANY PRACTICE EXAMS AND RETURN THEM WITH FEEDBACK.