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This course includes:

  • 2 hours on-demand video
  • 56 articles
  • Full lifetime access
  • Access on mobile and TV
Teaching & Academics Math Calculus

Algebra Foundations for Calculus

Learn exactly what you need to in order to be successful in Calculus
Rating: 4.2 out of 54.2 (15 ratings)
1,281 students
Created by Katie Kormanik
Last updated 5/2020
English
English [Auto]
30-Day Money-Back Guarantee

What you'll learn

  • Solve equations and inequalities involving exponents, logarithms, trigonometric functions
  • Graph polynomials and exponential, logarithmic, and trigonometric functions
  • Define and use the derivative--the most important concept in Calculus--to better understand how functions behave
  • Use limits to graph functions and find the derivative
  • Find sums of finite and infinite series

Requirements

  • Students should know the order of operations, basic arithmetic, and how to evaluate functions at a particular value
  • Students should have paper and pencil handy as they work through the course so that they can attempt the exercises and check their answers

Description

Welcome to Algebra Foundations for Calculus! In this course, you'll learn the foundational Algebra principles needed to be successful in Calculus.

Instructors:

  • Arun Sharma, PhD, Calculus professor at UC Berkeley
    After majoring in math, Arun got his PhD in pure mathematics from UC Berkeley in 2009. Since 2010 he has been teaching introductory math classes at UC Berkeley. Because of this, he intimately understands the areas in which students struggle. He feels many students entering college math classes are not as prepared in Algebra as they should be. Because of this, he is excited to offer this course to help ensure students succeed in Calculus and beyond. A fun fact about Arun is that he is highly ranked in chess and runs the US Chess League.

  • Katie Kormanik, CEO, TURN THE WHEEL
    Katie designs the courses, selects the experts and leaders the courses feature, and creates all the engaging content that you’ll see when you sign up. She is passionate about education and particularly excited about the potential of online learning. She has designed courses for Udacity, Stanford Graduate School of Business, and McKinsey Academy. Click here to see samples of her work. She has consulted for a number of education non-profits, start-ups, and for-profit companies on product development, curriculum development, pedagogy, and investments in edtech. And of course, she has been an educator in a number of capacities, from tutoring to teaching supplemental college courses, after-school programs, and summer school programs. Her two greatest passions are learning and making learning fun for others.

In this course, you'll watch videos in which Arun and Katie explain concepts and work through examples. We also provide many practice exercises so you can solidify what you're learning. Remember, learning math is just like learning a language, and the goal of this course is to make you fluent. Or, at least conversational. :)

A few tips as you work through this course:

  • Re-watch the videos to refresh your memory

  • Keep a pen and paper with you so you can do the exercises

  • Pause the videos occasionally to give you time to process the concepts

  • There's no need for calculators. This course is less about performing basic calculations and more about understanding the principles


Who this course is for:

  • This course is meant for anyone preparing to take Calculus, as well as anyone who would like a foundational understanding of pure mathematics
  • This course is NOT meant for those who seek to learn applied mathematics (for these students, I recommend our textbook Street-Smart Stats: A Friendly Introduction to Statistical Research Methods)

Course content

5 sections • 84 lectures • 2h 2m total length

  • Preview02:10

  • About the course
    00:44
  • Preview01:05
  • Preview03:41
  • Exercises: Compute expressions
    3 questions
  • Solutions: Compute expressions
    00:00
  • Preview04:40
  • Exercises: Find equations of lines and calculate slope
    00:18
  • Solutions: Find equations of lines and calculate slope
    00:00
  • Why is the slope important in Calculus?
    06:13
  • Exercises: Graph the derivative
    00:14
  • Solutions: Graph the derivative
    00:00
  • Simplifying rational expressions
    04:13
  • Exercises: Simplifying rational expressions
    00:02
  • Solutions: Simplifying rational expressions
    00:00
  • Simplifying logarithmic expressions
    05:22
  • Exercises: Simplifying logarithmic expressions
    00:03
  • Solutions: Simplifying logarithmic expressions
    00:00
  • Trig basics and the unit circle
    05:04
  • Exercises: Find sine, cosine, and tangent
    00:02
  • Solutions: Find sine, cosine, and tangent
    00:00

  • Why solve equations?
    00:59
  • Solving equations: Quadratics
    04:24
  • Exercises: Solve quadratic equations
    00:08
  • Solutions: Solve quadratic equations
    00:00
  • Solving equations: Absolute values
    07:06
  • Exercises: Solve equations involving absolute value
    00:04
  • Solutions: Solve equations involving absolute value
    00:00
  • Solving equations: Polynomials
    05:37
  • Exercises: Solve polynomial equations
    00:08
  • Solutions: Solve polynomial equations
    00:00
  • Solving equations: Rational expressions
    02:54
  • Exercises: Solve equations involving rational expressions
    00:04
  • Solutions: Solve equations involving rational expressions
    00:00
  • Solving equations: Exponents
    04:01
  • Exercises: Solve exponential equations
    00:03
  • Solutions: Solve exponential equations
    00:00
  • Solving equations: Logs
    04:37
  • Exercises: Solve logarithmic equations
    00:02
  • Solutions: Solve logarithmic equations
    00:00
  • Solving equations: Trigonometric functions
    04:24
  • Trig identities
    00:06
  • Exercises: Solve trigonometric equations
    00:03
  • Solutions: Solve trigonometric equations
    00:00
  • Why solve inequalities?
    00:29
  • Solving inequalities
    04:32
  • Exercises: Solve inequalities
    00:00
  • Solutions: Solve inequalities
    00:00

  • Introduction to graphing
    00:17
  • Parent functions
    05:05
  • Exercises: Graph each translation
    00:03
  • Solutions: Graph each translation
    00:00
  • Domain
    03:54
  • Exercises: Find the domain
    00:01
  • Solutions: Find the domain
    00:00
  • Graphing polynomials
    03:54
  • Exercises: Graph polynomials
    00:14
  • Solutions: Graph polynomials
    00:00
  • Graphing rational functions
    05:52
  • Exercises: Graph rational functions
    00:05
  • Solutions: Graph rational functions
    00:00
  • Logarithmic and exponential functions
    02:21
  • Exercises: Graph logarithmic and exponential functions
    00:01
  • Solutions: Graph logarithmic and exponential functions
    00:00
  • Graph trigonometric functions
    02:31
  • Exercises: Graph trigonometric functions
    00:00
  • Solutions: Graph trigonometric functions
    00:00
  • Piecewise functions
    00:00

  • Introduction to limits and series
    00:16
  • Limits
    03:12
  • Use limits to find the derivative
    03:18
  • Exercises: Find the derivative
    00:00
  • Solutions: Find the derivative
    00:00
  • Introduction to sequences and series
    00:00
  • Arithmetic series
    07:26
  • Exercises: Arithmetic series
    00:00
  • Solutions: Arithmetic series
    00:00
  • Finite geometric series
    04:30
  • Exercises: Finite geometric series
    00:00
  • Solutions: Finite geometric series
    00:00
  • Infinite geometric series
    04:18
  • Exercises: Infinite geometric series
    00:00
  • Solutions: Infinite geometric series
    00:00
  • Course close
    00:44
  • Before you go...
    00:38

Instructor

Katie Kormanik
Friendly online courses
Katie Kormanik
  • 4.1 Instructor Rating
  • 257 Reviews
  • 6,343 Students
  • 5 Courses

Hi! I love creating online courses and instructional materials on topics I love. So far, I've written a statistics textbook (Street-Smart Stats: A Friendly Introduction to Statistical Research Methods) and created an introductory chess course, a penmanship course, and an algebra course that focuses on topics that are essential in understanding calculus. 

To actually pay the bills, I run an instructional design consulting firm, TURN THE WHEEL, that helps organizations create digital learning experiences for their clients, customers, and workforce. These courses have much larger budgets than the ones I make by myself. For one thing, we do professional video shoots rather than filming on my iPhone, as I've done for my own personal courses. 

I love both creating my own courses--my side hobby--and working with big organizations. I love having the creative control to design curricula on topics I'm passionate about, and I love working with people to design courses that meet their needs (and learning a lot from the subject-matter experts with whom I collaborate). 

Another side project is creating a mobile learning platform that anyone can use to both create and take courses directly from their phone. I'm hoping this will empower people all over the world who don't have computers to create learning materials that will benefit their local communities and beyond.

I'm really passionate about online learning, and am especially excited to see how VR and AR revolutionize the way we learn. 

Thanks for reading!

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