Introduction to Calculus 3: Infinite Sequences and Series

Investigate infinite sequences and test for convergence of infinite series
What you'll learn
Express a sequence as an order of numbers
Express an order of numbers as a sequence
Determine whether a sequence converges or diverges
Prove whether a sequence is monotonic or bounded
Find the convergence of a sequence
Express a series in sigma notation
Find the sum of a geometric or telescoping series
Test for the convergence of a series using the Test for Divergence, Integral Test, Comparison/Limit Comparison Tests, Alternating Test, Root and Ratio Tests
Estimate the Sum of a Series
Estimate the Sum of an Alternating Series
Find the radius of convergence and interval of convergence of a power series
Represent a function as a Taylor Series and Maclaurin Series
Estimate how close the function is to its Taylor series representation using the Taylor's Inequality
Apply the Taylor polynomials
Requirements
Precalculus (algebra, trigonometry, and functions)
Calculus 1 (limits and derivatives)
Calculus 2 (integrals)
Description
HOW THIS COURSE WORK:
This course, Introduction to Calculus 3: Infinite Sequences and Series, includes the first three sections of my complete course in Calculus 3, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and theorems. The course is organized into the following topics:
Section 2: Infinite Sequences
Sequences
Convergence of a Sequence
Monotonic and/or Bounded Sequence
Section 3: Infinite Series
Series
Geometric Series
Telescoping Series
Harmonic Series
1. Test for Divergence (to be updated)
2. Integral Test (to be updated)
Estimating the Sum of a Series (to be updated)
3. Comparison Test (to be updated)
4. Limit Comparison Test (to be updated)
5. Alternating Test (to be updated)
Estimating the Sum of an Alternating Series (to be updated)
Absolute Convergence (to be updated)
6. Ratio Test (to be updated)
7. Root Test (to be updated)
Section 4: Power Series
Power Series (to be updated)
Radius of Convergence and Interval of Convergence (to be updated)
Representations of Functions as Power Series (to be updated)
Taylor Series and Maclaurin Series (to be updated)
Taylor's Inequality (to be updated)
Method 1: Direct Computation (to be updated)
Method 2: Use Term-by-term Differentiation and Integration (to be updated)
Method 3: Use Summation, Multiplication, and Division of Power Series (to be updated)
Applications of Taylor Polynomials (to be updated)

CONTENT YOU WILL GET INSIDE EACH SECTION:
Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.
Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).
Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.

HIGHLIGHTS:
#1: Downloadable lectures so you can watch whenever and wherever you are.
#2: Downloadable lecture notes and some extra notes so you can review the lectures if you don’t have a device to watch or listen to the recordings.
#3: Three complete problem sets with solutions (1 at the end of each section) for you to do more practices.
#4: Step-by-step guide to help you solve problems.

See you inside the course!
- Gina :)

Who this course is for:
Anyone who has completed Calculus 1 and Calculus 2 and wants to learn some more advanced calculus
Current Calculus 3 students who are looking for extra help outside school
Anyone who is not in the science stream but wants to study calculus for fun

More Info