Algebra Foundations for Calculus
- 2 hours on-demand video
- 57 articles
- Full lifetime access
- Access on mobile and TV
- Certificate of Completion
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- 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
- 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
Welcome to Algebra Foundations for Calculus! In this course, you'll learn the foundational Algebra principles needed to be successful in Calculus.
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
- 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)
This course prepares you for advanced math courses, namely Calculus. But what is Calculus? Arun and Katie describe this special field of mathematics.
One of the first steps to being successful in mathematics is the ability to properly notate mathematical ideas. Katie and Arun show examples of how you should write different mathematical expressions, especially using symbols such as parentheses.
Trigonometric (trig) functions are crucial to understand as well. Unlike the other functions you’ve learned about, trig functions are used to describe the relationships between angle measurements and the sides of the triangles that contain the angles. Katie describes how to use the Unit Circle to find sin(?), cos(?), and tan(?), where ? is the angle measurement for common angles, and how to describe these angles in degrees or radians.
Solving inequalities is the last concept you’ll learn in this lesson. Solving them is very similar to solving equations (and you apply largely the same techniques), except now your solutions will involve a range of values. To find this range, you first have to be able to solve equalities, which is why you learned that first. Before diving into some examples, read why being able to solve inequalities is so important.
(Note: The point is not to graph them perfectly, but to be able to roughly visualize it, particularly where it’s increasing, decreasing, positive, negative, and where it intersects the x-axis. Remember that f’(x) tells us where the function is increasing and decreasing.)