Calculus 2
SAT Score Range
•
20 sessions
•
AC
DB
CF
+11
This series ended on November 18, 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 intermidiate class of Calculus by working problems together in each class. The topics will cover integration, its applications, techniques for it, and introduction to differential equations, sequences, series, power series, parametric equations, and polar coordinates.
You should be knowledgeable in limits and derivatives before enrolling in this series.
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 or have taken. Attendance to all classes is encouraged since (as all topics in math) they build upon each other.
SESSION 1
31
Aug
SESSION 1
Orientation
Orientation
Tue 10:30 PM - Wed, 12:30 AM UTCAug 31, 10:30 PM - Sep 1, 12:30 AM UTC
This is a session to briefly introduce each other, especially those intending to stay for the entire series. We will then go over an initroduction to integrals by approximating areas under a curve and going throught the definition of the definite integral.
SESSION 2
3
Sep
SESSION 2
Integration and accumulation of change
Integration and accumulation of change
Fri 12:30 AM - 2:30 AM UTCSep 3, 12:30 AM - 2:30 AM UTC
We will go through the fundamental theorem of calculus, integration formulas, and the net change theorem.
SESSION 3
7
Sep
SESSION 3
Integration and accumulation of change
Integration and accumulation of change
Tue 10:30 PM - Wed, 12:30 AM UTCSep 7, 10:30 PM - Sep 8, 12:30 AM UTC
INTEGRATION
The Fundamental Theorem of Calculus
- Describe the meaning of the Mean Value Theorem for Integrals. - State the meaning of the Fundamental Theorem of Calculus, Part 1. - Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals. - State the meaning of the Fundamental Theorem of Calculus, Part 2. - Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals. - Explain the relationship between differentiation and integration.
Integration Formulas and the Net Change Theorem
- Apply the basic integration formulas. - Explain the significance of the net change theorem. - Use the net change theorem to solve applied problems. - Apply the integrals of odd and even functions.
SESSION 4
9
Sep
SESSION 4
Integration and accumulation of change
Integration and accumulation of change
Thu 10:30 PM - Fri, 12:30 AM UTCSep 9, 10:30 PM - Sep 10, 12:30 AM UTC
INTEGRATION
Substitution
- Use substitution to evaluate indefinite integrals. - Use substitution to evaluate definite integrals.
SESSION 5
14
Sep
SESSION 5
Integration and accumulation of change
Integration and accumulation of change
Tue 10:30 PM - Wed, 12:30 AM UTCSep 14, 10:30 PM - Sep 15, 12:30 AM UTC
INTEGRATION
Integrals Involving Exponential and Logarithmic Functions
- Integrate functions involving exponential functions. - Integrate functions involving logarithmic functions.
Integrals Resulting in Inverse Trigonometric Functions
- Integrate functions resulting in inverse trigonometric functions
SESSION 6
16
Sep
SESSION 6
Applications of integration
Applications of integration
Thu 10:30 PM - Fri, 12:30 AM UTCSep 16, 10:30 PM - Sep 17, 12:30 AM UTC
APPLICATIONS OF INTEGRATION
Areas between Curves
- Determine the area of a region between two curves by integrating with respect to the independent variable. - Find the area of a compound region. - Determine the area of a region between two curves by integrating with respect to the dependent variable.
Determining Volumes by Slicing
- Determine the volume of a solid by integrating a cross-section (the slicing method). - Find the volume of a solid of revolution using the disk method. - Find the volume of a solid of revolution with a cavity using the washer method.
SESSION 7
22
Sep
SESSION 7
Applications of integration
Applications of integration
Wed 10:30 PM - Thu, 12:30 AM UTCSep 22, 10:30 PM - Sep 23, 12:30 AM UTC
APPLICATIONS OF INTEGRATION
Volumes of Revolution: Cylindrical Shells
- Calculate the volume of a solid of revolution by using the method of cylindrical shells. - Compare the different methods for calculating a volume of revolution.
SESSION 8
23
Sep
SESSION 8
Applications of integration
Applications of integration
Thu 10:30 PM - Fri, 12:30 AM UTCSep 23, 10:30 PM - Sep 24, 12:30 AM UTC
APPLICATIONS OF INTEGRATION
Arc Length of a Curve and Surface Area
- Determine the length of a curve, y=f(x), between two points. - Determine the length of a curve, x=g(y), between two points. - Find the surface area of a solid of revolution.
SESSION 9
1
Oct
SESSION 9
Applications of integration
Applications of integration
Fri 2:30 PM - 4:30 PM UTCOct 1, 2:30 PM - 4:30 PM UTC
APPLICATIONS OF INTEGRATION
Physical Applications
- Determine the mass of a one-dimensional object from its linear density function. - Determine the mass of a two-dimensional circular object from its radial density function. - Calculate the work done by a variable force acting along a line. - Calculate the work done in pumping a liquid from one height to another. - Find the hydrostatic force against a submerged vertical plate.
Moments and Centers of Mass
- Find the center of mass of objects distributed along a line. - Locate the center of mass of a thin plate. - Use symmetry to help locate the centroid of a thin plate. - Apply the theorem of Pappus for volume.
SESSION 10
2
Oct
SESSION 10
Applications of integration
Applications of integration
Sat 2:30 PM - 4:30 PM UTCOct 2, 2:30 PM - 4:30 PM UTC
APPLICATIONS OF INTEGRATION
Integrals, Exponential Functions, and Logarithms
- Write the definition of the natural logarithm as an integral. - Recognize the derivative of the natural logarithm. - Integrate functions involving the natural logarithmic function. - Define the number e through an integral. - Recognize the derivative and integral of the exponential function. - Prove properties of logarithms and exponential functions using integrals. - Express general logarithmic and exponential functions in terms of natural logarithms and exponentials.
Exponential Growth and Decay
- Use the exponential growth model in applications, including population growth and compound interest. - Explain the concept of doubling time. - Use the exponential decay model in applications, including radioactive decay and Newton’s law of cooling. - Explain the concept of half-life.
SESSION 11
8
Oct
SESSION 11
Applications of integration
Applications of integration
Fri 3:00 PM - 5:00 PM UTCOct 8, 3:00 PM - 5:00 PM UTC
APPLICATIONS OF INTEGRATION
Calculus of the Hyperbolic Functions
- Apply the formulas for derivatives and integrals of the hyperbolic functions. - Apply the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals. - Describe the common applied conditions of a catenary curve.
SESSION 12
9
Oct
SESSION 12
Integration and accumulation of change
Integration and accumulation of change
Sat 2:30 PM - 4:30 PM UTCOct 9, 2:30 PM - 4:30 PM UTC
TECHNIQUES OF INTEGRATION
Integration by Parts
- Recognize when to use integration by parts. - Use the integration-by-parts formula to solve integration problems. - Use the integration-by-parts formula for definite integrals.
Trigonometric Integrals
- Solve integration problems involving products and powers of sinx and cosx. - Solve integration problems involving products and powers of tanx and secx. - Use reduction formulas to solve trigonometric integrals.
SESSION 13
15
Oct
SESSION 13
Integration and accumulation of change
Integration and accumulation of change
Fri 2:30 PM - 4:30 PM UTCOct 15, 2:30 PM - 4:30 PM UTC
TECHNIQUES OF INTEGRATION
Trigonometric Substitution
- Solve integration problems involving the square root of a sum or difference of two squares.
Partial Fractions
- Integrate a rational function using the method of partial fractions. - Recognize simple linear factors in a rational function. - Recognize repeated linear factors in a rational function. - Recognize quadratic factors in a rational function.
SESSION 14
16
Oct
SESSION 14
Integration and accumulation of change
Integration and accumulation of change
Sat 2:30 PM - 4:30 PM UTCOct 16, 2:30 PM - 4:30 PM UTC
TECHNIQUES OF INTEGRATION
Other Strategies for Integration
- Use a table of integrals to solve integration problems. - Use a computer algebra system (CAS) to solve integration problems.
Numerical Integration
- Approximate the value of a definite integral by using the midpoint and trapezoidal rules. - Determine the absolute and relative error in using a numerical integration technique. - Estimate the absolute and relative error using an error-bound formula. - Recognize when the midpoint and trapezoidal rules over- or underestimate the true value of an integral. - Use Simpson’s rule to approximate the value of a definite integral to a given accuracy.
SESSION 15
29
Oct
SESSION 15
Integration and accumulation of change
Integration and accumulation of change
Fri 2:30 PM - 4:30 PM UTCOct 29, 2:30 PM - 4:30 PM UTC
TECHNIQUES OF INTEGRATION
Improper Integrals
- Evaluate an integral over an infinite interval. - Evaluate an integral over a closed interval with an infinite discontinuity within the interval. - Use the comparison theorem to determine whether a definite integral is convergent.
SESSION 16
30
Oct
SESSION 16
Differential equations
Differential equations
Sat 2:30 PM - 4:30 PM UTCOct 30, 2:30 PM - 4:30 PM UTC
INTRODUCTION TO DIFFERENTIAL EQUATIONS
Basics of Differential Equations
- Identify the order of a differential equation. - Explain what is meant by a solution to a differential equation. - Distinguish between the general solution and a particular solution of a differential equation. - Identify an initial-value problem. - Identify whether a given function is a solution to a differential equation or an initial-value problem.
Direction Fields and Numerical Methods
- Draw the direction field for a given first-order differential equation. - Use a direction field to draw a solution curve of a first-order differential equation. - Use Euler’s Method to approximate the solution to a first-order differential equation.
SESSION 17
5
Nov
SESSION 17
Differential equations
Differential equations
Fri 2:30 PM - 4:30 PM UTCNov 5, 2:30 PM - 4:30 PM UTC
INTRODUCTION TO DIFFERENTIAL EQUATIONS
Separable Equations
- Use separation of variables to solve a differential equation. - Solve applications using separation of variables.
SESSION 18
6
Nov
SESSION 18
Differential equations
Differential equations
Sat 2:30 PM - 4:30 PM UTCNov 6, 2:30 PM - 4:30 PM UTC
INTRODUCTION TO DIFFERENTIAL EQUATIONS
The Logistic Equation
- Describe the concept of environmental carrying capacity in the logistic model of population growth. - Draw a direction field for a logistic equation and interpret the solution curves. - Solve a logistic equation and interpret the results.
First-order Linear Equations
- Write a first-order linear differential equation in standard form. - Find an integrating factor and use it to solve a first-order linear differential equation. - Solve applied problems involving first-order linear differential equations.
SESSION 19
12
Nov
SESSION 19
Infinite sequences and series
Infinite sequences and series
Fri 3:30 PM - 5:30 PM UTCNov 12, 3:30 PM - 5:30 PM UTC
SEQUENCES AND SERIES
Sequences
- Find the formula for the general term of a sequence. - Calculate the limit of a sequence if it exists. - Determine the convergence or divergence of a given sequence.
SESSION 20
13
Nov
SESSION 20
Infinite sequences and series
Infinite sequences and series
Sat 3:30 PM - 5:30 PM UTCNov 13, 3:30 PM - 5:30 PM UTC
SEQUENCES AND SERIES
Infinite Series
- Explain the meaning of the sum of an infinite series. - Calculate the sum of a geometric series. - Evaluate a telescoping series.
The Divergence and Integral Tests
- Use the divergence test to determine whether a series converges or diverges. - Use the integral test to determine the convergence of a series. - Estimate the value of a series by finding bounds on its remainder term.