# Introduction to Calculus

*Watch all ten videos and take the quizzes to earn your certificate. *

**Calculus ****Video 1****: The Idea of Limits**

* **In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus.*

After you watch the video, **CLICK HERE FOR THE QUIZ over the Idea of Limits.**

**Calculus ****Video 2****: The Limit Laws **

*In the Limit Laws video, we introduce the limit laws and discuss how to use them in order to compute limits.*

After you watch the video, * CLICK HERE FOR THE QUIZ over the Limit Laws*.

**Calculus ****Video 3****: Computing Limits in Practice **

*In the Computing Limits in Practice video, we compute some limits in practice; though simple limits of nice (continuous) functions at a point can be computed by plugging in function value at that point, this cannot always be done, notably when the function is undefined at that point. We go through some examples of how to use algebra and factoring to overcome this issue.*

After you watch *the Computing Limits in Practice video*, **CLICK HERE FOR QUIZ 3.**

**Calculus Video 4: Non-Existent Limits **

In **Calculus Video 4: Non-Existent Limits**, we discuss the fact that limits of functions need not necessarily exist. We go through some examples and introduce the idea of left and right-handed limits to give us a computational tool to help determine whether or not limits exist.

After you watch the video, **CLICK HERE FOR QUIZ 4**

**Calculus Video 5: Infinite Limits**

In **Calculus Video 5: Infinite Limits**, we discuss infinite limits, which is to say when functions have singularities or, in other words, vertical asymptotes. We give some examples of how to detect and compute these limits in practice.

After you watch the video, **CLICK HERE FOR QUIZ 5**

**Calculus Video 6: Continuity and Composition of Limits**

In this video, we introduce another powerful limit law: the composition of limits. We show how this powerful tool can vastly increase the number of limits we are able to compute.

After you watch the video, **CLICK HERE FOR QUIZ 6**

**Calculus ****Video 7: Limits at Infinity and Horizontal Asymptotes**

In this video, we discuss the notion of limits at infinity or, in other words, when functions have horizontal asymptotes. In addition to introducing this idea, we also discuss how to compute these limits, notably how our familiar limit laws also apply in this case.

After you watch the video, ** CLICK HERE FOR THE QUIZ for Limits at Infinity**.

**Calculus Video 8:: Supplementary Limit Laws and “Switching Things Around” **

In **Calculus Video 8:: Supplementary Limit Laws and “Switching Things Around”**, we discuss a tricky limit law involving how and why we can swap x for 1/x and vice versa when computing a limit. Despite being a bit on the subtle side, this is a powerful technique that can be used to compute some very difficult limits.

After you watch the video, * CLICK HERE FOR THE QUIZ for Supplementary Limit Laws*.

**Calculus Video 9: The Squeeze Theorem **

*In The Squeeze Theorem video, we discuss the Squeeze Theorem which is a theoretical tool that nonetheless gives us a lot of computational power. In a nutshell, it allows us to leverage a clever use of inequalities to compute limits that we otherwise could not be able to deal with*.

After you watch The Squeeze Theorem video, * CLICK HERE FOR THE QUIZ over the Squeeze Theorem*.

**Calculus Video 10: The Intermediate Value Theorem**

In this video, we discuss the Intermediate Value Theorem which is a fact that governs the behavior of continuous functions. This is an important theoretical fact and is one of the most important properties of the real numbers themselves. On the other hand, this theorem can also be used as a tool to determine when and approximately where potentially very complicated functions have roots.

After you watch the video, * CLICK HERE FOR THE QUIZ over the Intermediate Value Theorem*.

## After you watch all 10 videos and take the quizzes, **CLICK HERE FOR THE CERTIFICATE**.

*Your STEM Certificate will come from purduestemdegree@ gmail.com. Make sure it is not blocked by your school. It is an unmonitored email that is ONLY used for these certificates. *

### The Introduction to Calculus STEM Degree was created in collaboration with Dr. Daniel Johnstone, Department of Mathematics, Purdue University, West Lafayette, IN