Calculus 1
SAT Score Range
•
9 sessions
•
SM
KL
SA
+17
This series ended on October 3, 2021. All 1:1 and group chats related to this series are disabled 7 days after the last session.
About
We will go through an introductory class of Calculus by working problems together in each class. The topics will cover functions, limits, derivatives, integrals, and their applications.
The session times are set to two hours, estimating the time you might need to understand the entire topic. It might take less time than that, it will depend on how well is everyone getting the topic.
Tutored by
Schedule
✋ ATTENDANCE POLICY
You are free to attend any session you wish to. Attendance is not mandatory since the class is intended to compliment a calculus class you might be taking. Attendance to all classes is encouraged since (as all topics in math) they build upon each other.
SESSION 1
30
Aug
SESSION 1
Orientation
Orientation
Mon 10:30 PM - Tue, 12:30 AM UTCAug 30, 10:30 PM - Aug 31, 12:30 AM UTC
This is a session to briefly introduce each other, especially those intending to stay for the entire class. We will also have a review on functions and their graphs.
SESSION 2
2
Sep
SESSION 2
Review
Review
Thu 12:30 AM - 2:30 AM UTCSep 2, 12:30 AM - 2:30 AM UTC
This session will continue the review over functions. It will cover trigonometric, inverse, exponential, and logarithmic functions.
SESSION 3
8
Sep
SESSION 3
Review
Review
Wed 10:30 PM - Thu, 12:30 AM UTCSep 8, 10:30 PM - Sep 9, 12:30 AM UTC
FUNCTIONS AND GRAPHS
Trigonometric Functions
- Convert angle measures between degrees and radians. - Recognize the triangular and circular definitions of the basic trigonometric functions. - Write the basic trigonometric identities. - Identify the graphs and periods of the trigonometric functions. - Describe the shift of a sine or cosine graph from the equation of the function.
Inverse Functions
- Determine the conditions for when a function has an inverse. - Use the horizontal line test to recognize when a function is one-to-one. - Find the inverse of a given function. - Draw the graph of an inverse function. - Evaluate inverse trigonometric functions.
SESSION 4
13
Sep
SESSION 4
Review
Review
Mon 10:30 PM - Tue, 12:30 AM UTCSep 13, 10:30 PM - Sep 14, 12:30 AM UTC
FUNCTIONS AND GRAPHS
Exponential and Logarithmic Functions
-Identify the form of an exponential function. - Explain the difference between the graphs of xb and bx. - Recognize the significance of the number e. - Identify the form of a logarithmic function. - Explain the relationship between exponential and logarithmic functions. - Describe how to calculate a logarithm to a different base. - Identify the hyperbolic functions, their graphs, and basic identities.
SESSION 5
15
Sep
SESSION 5
Limits and continuity
Limits and continuity
Wed 10:30 PM - Thu, 12:30 AM UTCSep 15, 10:30 PM - Sep 16, 12:30 AM UTC
LIMITS
A Preview of Calculus
- Describe the tangent problem and how it led to the idea of a derivative. - Explain how the idea of a limit is involved in solving the tangent problem. - Recognize a tangent to a curve at a point as the limit of secant lines. - Identify instantaneous velocity as the limit of average velocity over a small time interval. - Describe the area problem and how it was solved by the integral. - Explain how the idea of a limit is involved in solving the area problem. - Recognize how the ideas of limit, derivative, and integral led to the studies of infinite series and multivariable calculus.
The Limit of a Function
- Using correct notation, describe the limit of a function. - Use a table of values to estimate the limit of a function or to identify when the limit does not exist. - Use a graph to estimate the limit of a function or to identify when the limit does not exist. - Define one-sided limits and provide examples. - Explain the relationship between one-sided and two-sided limits. - Using correct notation, describe an infinite limit. - Define a vertical asymptote.
SESSION 6
24
Sep
SESSION 6
Limits and continuity
Limits and continuity
Fri 4:00 PM - 6:00 PM UTCSep 24, 4:00 PM - 6:00 PM UTC
LIMITS
The Limit Laws
- Recognize the basic limit laws. - Use the limit laws to evaluate the limit of a function. - Evaluate the limit of a function by factoring. - Use the limit laws to evaluate the limit of a polynomial or rational function. - Evaluate the limit of a function by factoring or by using conjugates. - Evaluate the limit of a function by using the squeeze theorem.
SESSION 7
25
Sep
SESSION 7
Limits and continuity
Limits and continuity
Sat 4:00 PM - 6:00 PM UTCSep 25, 4:00 PM - 6:00 PM UTC
LIMITS
Continuity
- Explain the three conditions for continuity at a point. - Describe three kinds of discontinuities. - Define continuity on an interval. - State the theorem for limits of composite functions. - Provide an example of the intermediate value theorem.
The Precise Definition of a Limit
- Describe the epsilon-delta definition of a limit. - Apply the epsilon-delta definition to find the limit of a function. - Describe the epsilon-delta definitions of one-sided limits and infinite limits. - Use the epsilon-delta definition to prove the limit laws.
SESSION 8
28
Sep
SESSION 8
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Tue 2:30 PM - 4:30 PM UTCSep 28, 2:30 PM - 4:30 PM UTC
DERIVATIVES
Defining the Derivative
- Recognize the meaning of the tangent to a curve at a point. - Calculate the slope of a tangent line. - Identify the derivative as the limit of a difference quotient. - Calculate the derivative of a given function at a point. - Describe the velocity as a rate of change. - Explain the difference between average velocity and instantaneous velocity. - Estimate the derivative from a table of values.
SESSION 9
30
Sep
SESSION 9
Differentiation: definition and basic derivative rules
Differentiation: definition and basic derivative rules
Thu 6:30 PM - 8:30 PM UTCSep 30, 6:30 PM - 8:30 PM UTC
DERIVATIVES
- Define the derivative function of a given function. - Graph a derivative function from the graph of a given function. - State the connection between derivatives and continuity. - Describe three conditions for when a function does not have a derivative. - Explain the meaning of a higher-order derivative.
Differentiation Rules
- State the constant, constant multiple, and power rules. - Apply the sum and difference rules to combine derivatives. - Use the product rule for finding the derivative of a product of functions. - Use the quotient rule for finding the derivative of a quotient of functions. - Extend the power rule to functions with negative exponents. - Combine the differentiation rules to find the derivative of a polynomial or rational function.