September 10, 2023

Ace Calculus 3 in 16 Hours (The Complete Course)

Study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions
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
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
Requirements
Calculus 1 (limits and derivatives)
Calculus 2 (integrals)
Familiarity with vector geometry or linear algebra
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 SequencesConvergence of a sequenceProperties of a sequence: monotonic and boundedSection 3: Infinite SeriesSpecial series: geometric series, telescoping series, harmonic seriesSix convergence/divergence tests: test for divergence, integral test, comparison test, limit comparison test, alternating test, ratio test, and root testSection 4: Power SeriesTaylor series and Maclaurin seriesTaylor’s inequalityThree methods: direct computation, use term-by-term differentiation/integration, and use summation, multiplication, and division of power seriesSection 5: Vectors and the Geometry of SpaceVectorsOperations of vectors: the dot product, projection, and cross productEquations of lines and planes in 3DSurfaces in 3DSection 6: Vector FunctionsDerivative and integral of vector functionsThe arc length and curvatureFrenet-Serret EquationsMotion in Space: Velocity and AccelerationSection 7: Partial DerivativesMultivariable functionsPartial derivativesInterpretations of partial derivativesTangent planesLinear approximationsChain ruleDifferentiationThe gradient vector and directional derivativesFinding extreme values of a multivariable functionLagrange multipliersSection 8: Multiple IntegralsDouble Riemann sumEstimating the volume under a surfaceIterated/double integralsDouble integral over general regionsDouble integrals in polar coordinatesSurface areaCONTENT 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 successLifetime 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 🙂
Who this course is for
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
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