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.
Series Details
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.
✋ 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.
Dates
August 31 - November 13
Learners
14 / 15
Total Sessions
20
About the Tutor
BL
SL
I am a Guatemalan living in the U.S. as an international student. I have always loved math and sciences, and I am always keen to help people who need help with them. I hope to be able to show you how beautiful math is.
View Samuel L's Profile
Upcoming Sessions
0
Past Sessions
20
31
Aug
O
Session 1
Orientation
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.
3
Sep
Ic
Session 2
Integration and accumulation of change
We will go through the fundamental theorem of calculus, integration formulas, and the net change theorem.
7
Sep
Ic
Session 3
Integration and accumulation of change
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.
9
Sep
Ic
Session 4
Integration and accumulation of change
INTEGRATION
Substitution
- Use substitution to evaluate indefinite integrals. - Use substitution to evaluate definite integrals.
14
Sep
Ic
Session 5
Integration and accumulation of change
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
16
Sep
Ai
Session 6
Applications of integration
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.
22
Sep
Ai
Session 7
Applications of integration
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.
23
Sep
Ai
Session 8
Applications of integration
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.
1
Oct
Ai
Session 9
Applications of integration
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.
2
Oct
Ai
Session 10
Applications of integration
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.
8
Oct
Ai
Session 11
Applications of integration
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.
9
Oct
Ic
Session 12
Integration and accumulation of change
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.
15
Oct
Ic
Session 13
Integration and accumulation of change
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.
16
Oct
Ic
Session 14
Integration and accumulation of change
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.
29
Oct
Ic
Session 15
Integration and accumulation of change
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.
30
Oct
De
Session 16
Differential equations
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.
5
Nov
De
Session 17
Differential equations
INTRODUCTION TO DIFFERENTIAL EQUATIONS
Separable Equations
- Use separation of variables to solve a differential equation. - Solve applications using separation of variables.
6
Nov
De
Session 18
Differential equations
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.
12
Nov
Is
Session 19
Infinite sequences and series
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.
13
Nov
Is
Session 20
Infinite sequences and series
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.