What you'll learn
Understanding what happens as a function approaches a point
Extedning the idea of "slope" from straight lines to all curves
Applying these slopes to explore the behavior of graphs
Using these tools in real-world applications
Requirements
Experience with algebra and trigonometry - take a look at our other courses if you need a refresher!
Description
A typical calculus 1 course covers two main topics: limits and derivatives.Limits describe what happens to a function near a specific point (but not necessarily at that point). The intimately-related topic of continuity is perhaps that most important underpinning the theorems of the mathematics of functions. You'll learn how to think about questions like:What does it mean to be "close" to a point?What can we learn about a function on an interval given that the curve is connected? Smooth?How do we know what happens in the neighborhood of dividing by zero?How can we combine limits and the algebra equation for slope to think about the slope of a curve?Derivatives are functions which describe the slope of a corresponding function. Once we can think about the behavior of the derivative, a whole range of applications present themselves! You'll learn how to think about questions like:How do we evaluate the slope of a line that isn't straight?What simplifications can we use in evaluating derivatives based on the different types of basic operations?What does it mean for the slope to be zero?How do derivatives of multiple related functions interrelate?What happens if you take the derivative of the derivative?Can't wait to get started! Calculus 1 is a gateway into a whole new realm of math and way of thinking. Let's go!
Overview
Section 1: Introduction
Lecture 1 Welcome to Calc 1: Limits & Deriviatives!
Lecture 2 Prerequisites in More Detail
Lecture 3 Big Picture Idea: Limits
Lecture 4 Big Picture Idea: Derivatives
Lecture 5 Getting Ready
Section 2: Limit Concepts
Lecture 6 Does it Exist?
Lecture 7 Piecewise Functions
Lecture 8 Absolute Value
Lecture 9 What is Continuity?
Lecture 10 The Intermediate Value Theorem
Section 3: Limit Solutions
Lecture 11 Conjugates
Lecture 12 The Squeeze Theorem
Lecture 13 End Behavior
Lecture 14 Slant Asymptotes
Lecture 15 The Difference Quotient
Section 4: Core Function Derivatives
Lecture 16 Quadratics
Lecture 17 Linearity of Difference Quotient
Lecture 18 The Power Rule
Lecture 19 The "Derivative" Formally
Lecture 20 Exponentials & Logarithms
Lecture 21 Trig & Inverse Trig
Section 5: Derivative Tools
Lecture 22 The Product & Quotient Rules
Lecture 23 The Chain Rule
Lecture 24 Putting These Together
Lecture 25 Implicit Differentiation
Section 6: Derivative Applications
Lecture 26 Extrema, Average Rate, & Mean Value
Lecture 27 The Second Derivative
Lecture 28 Exploring Rational Functions
Lecture 29 Related Rates
Lecture 30 Optimization
Lecture 31 Content Conclusion
Section 7: Practice Set A
Lecture 32 Set A Introduction
Lecture 33 Problem 1
Lecture 34 Problem 2
Lecture 35 Problem 3
Lecture 36 Problem 4
Lecture 37 Problem 5
Lecture 38 Problem 6
Lecture 39 Problem 7
Lecture 40 Problem 8
Lecture 41 Problem 9
Lecture 42 Problem 10
Lecture 43 Problem 11
Lecture 44 Problem 12
Lecture 45 Problem 13
Lecture 46 Problem 14
Lecture 47 Problem 15
Lecture 48 Problem 16
Lecture 49 Problem 17
Lecture 50 Problem 18
Section 8: Bonus Lecture
Lecture 51 Bonus Lecture: UpGrade University
Lovers and future lovers of math who are ready to learn by exploring concepts,Calc 1 serves as a gateway to lots of technical fields, and is a common early college course for these kinds of majors


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