Ace Calculus 3 in 16 Hours (The Complete Course)

HOW THIS COURSE WORK:

This course, Ace Calculus 3 in 16 Hours (The Complete Course), is intended to introduce students to the study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions. The course includes videos, notes from the 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, term-by-term differentiation/integration, and 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 integrals 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

• The 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 issues 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 resources 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 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 on the course!

- Gina :)