Ace Calculus 3 in 16 Hours (The Complete Course)

Study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions

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Description

HOW THIS COURSE WORK:

This course, Ace Calculus 3 in 16 Hours (The Complete Course), is intended to introduce the student to the study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions. The course includes videos, notes from whiteboard during lectures, and practice problem sets (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:

Section 2: Infinite Sequences

  • Convergence of a sequence

  • Properties of a sequence: monotonic and bounded

Section 3: Infinite Series

  • Special series: geometric series, telescoping series, harmonic series

  • Six convergence/divergence tests: test for divergence, integral test, comparison test, limit comparison test, alternating test, ratio test, and root test

Section 4: Power Series

  • Taylor series and Maclaurin series

  • Taylor’s inequality

  • Three methods: direct computation, use term-by-term differentiation/integration, and use summation, multiplication, and division of power series

Section 5: Vectors and the Geometry of Space

  • Vectors

  • Operations of vectors: the dot product, projection, and cross product

  • Equations of lines and planes in 3D

  • Surfaces in 3D

Section 6: Vector Functions

  • Derivative and integral of vector functions

  • The arc length and curvature

  • Frenet-Serret Equations

  • Motion in Space: Velocity and Acceleration

Section 7: Partial Derivatives

  • Multivariable functions

  • Partial derivatives

  • Interpretations of partial derivatives

  • Tangent planes

  • Linear approximations

  • Chain rule

  • Differentiation

  • The gradient vector and directional derivatives

  • Finding extreme values of a multivariable function

  • Lagrange multipliers

Section 8: Multiple Integrals

  • Double Riemann sum

  • Estimating the volume under a surface

  • Iterated/double integrals

  • Double integral over general regions

  • Double integrals in polar coordinates

  • Surface area


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 before moving on to the next section.


THINGS THAT ARE INCLUDED IN THE COURSE:

  • An instructor who truly cares about your success

  • Lifetime access to Ace Calculus 3 in 16 Hours (The Complete Course)


HIGHLIGHTS:

#1: Downloadable lectures so you can watch the videos whenever and wherever you are.

#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

#3: Seven problem sets at the end of each section (with solutions!) for you to do more practice.

#4: Step-by-step guide to help you solve problems.


See you inside the course!

- Gina :)

What You Will 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
  • Perform operations on vectors (dot product, projection, and cross product)
  • Recognize and understand equations of lines and planes in 3D
  • Recognize and sketch a surface function (a function of two variables)
  • Take the derivative and integral of a vector function
  • Find the arc length, curvature, and torsion of a vector function
  • Use and understand the Frenet-Serret equations
  • Sketch functions of two variables as surfaces and level curves
  • Take the partial derivative of a multivariable functions with respect to different variables
  • Use partial derivatives to find the equation of tangent planes
  • Apply the chain rule on multivariable functions
  • Find the gradient vector and directional derivatives
  • Maximize and minimize a multivariable function
  • Apply Lagrange multiplier method
  • Estimate the volume under a surface using double Riemann sum
  • Evaluate iterated integrals
  • Evaluate double integrals over general regions
  • Evaluate double integrals in polar coordinates
  • Find the surface are of a two-variable function over a region

Who Should Attend!

  • Anyone who has completed calculus 1 (limits and derivatives) and calculus 2 (integrals) and wants to learn some more advanced math
  • Current Calculus 3 students who are looking for extra help
  • Anyone who is not in the science stream but wants to study calculus for fun