## Course Notes

Below you will find notes and handouts that we have used in class, as well as some other useful stuff.

- Trig Unit Circle
- Are You Ready for Calculus? Questions
- Are You Ready for Calculus? Answers
- Section 2.1: Average Rate of Change
- Section 2.2: Rates of Change
- Section 2.3: Intuitive Derivative
- Section 2.4: Limits (Part 1)
- Section 2.6: Limit Rules
- Section 2.7: Some Basic Derivatives
- Sections 3.1 & 3.2: Power Rule and Derivatives of Linear Combinations
- Section 3.4: Derivatives of Products and Quotients
- Supplementary Exercises for Section 4.1: L’Hospital’s Rule
- Section 4.2: Function Analysis
- Section 4.4: Optimization (part 2)
- Section 4.7: Related Rates
- Section 5.5: Indefinite Integrals
- Section 5.3: The Fundamental Theorem of Calculus
- Section 5.4: Another Fundamental Theorem
- Section 5.6: Substitution
- Section 5.7: Integration by Parts
- Section 6.1: Falling Objects

## Calculus Videos

There are tons of calculus related videos out there. In fact, I’ve listed a few popular resources on the Course Resources page. Below, I will post links to videos that I feel are particularly relevant to our discussion of calculus. Most of the videos will come from MOOCulus.

- Introduction to WeBWorK.
**Note:**There are some inconsistencies in this video due to the fact that I made it for my Fall 2012 class. The version of WeBWorK has been upgraded, but it should still be useful. - What is a functions?
- Linear Functions
- Inverses of Functions
- When are two functions the same?
- How can more functions be made?
- What comes next? Derivatives?
- What is a tangent line?
- Why is the absolute value function not differentiable?
- A Motivating Example for Limits
- What is the limit of $\frac{x^2-1}{x-1}$ as $x$ approaches 1
- Four Examples of Limits
- What is a one-sided limit?
- Could a one-sided limit not exist?
- What does it mean for the limit of a function to equal infinity?
- What is the limit of $f(x)$ as $x$ approaches infinity?
- Four examples of limits at infinity
- What are asymptotes?
- Why is infinity not a number?
- What is the limit of $\frac{\sin(x)}{x}$ as $x$ approaches 0?
- What is the limit of $\sin(1/x)$ as $x$ approaches 0?
- What is the limit of a sum?
- What is the limit of a product?
- What is the limit of a quotient?
- What is the official definition of a limit?
- What does continuous mean?
- Slopes and derivatives
- What is the definition of the derivative?
- What information is recorded in the sign of the derivative?
- Why is a differentiable function necessarily continuous?
- What is the derivative of a constant multiple of $f(x)$?
- Why is the derivative of $x^2$ equal to $2x$?
- What is the derivative of $x^n$?
- How do we justify the power rule?
- What is the derivative of $x^3+x^2$?
- What is the derivative of $\sqrt{x+3}$?
- Why is the derivative of a sum the sum of the derivatives?
- What is the chain rule?
- How does one prove the chain rule?
- What is the derivative of a product?
- Morally why is the product rule true?
- What is the quotient rule?
- How can I remember the quotient rule?
- How do we prove the quotient rule?
- What is the derivative of a log?
- What is logarithmic differentiation?
- How can logarithms help to prove the product rule?
- What is the derivative of sine and cosine?
- What is the derivative of tangent?
- What are the derivatives of the other trig functions?
- What is the derivative of $\sin(x^2)$?
- How can derivatives help us compute limits?
- How can L’Hospital’s Rule help us with other indeterminate forms?
- Why does $f’$ positive imply that $f$ is increasing?
- What sorts of optimization problems will calculus help us solve?
- What is the extreme value theorem?
- How do I find the maximum and minimum values for $f$ on a given domain?
- Why do we have to bother checking endpoints?
- How can you build the best fence for your sheep?
- How large can $xy$ be if $x+y=24$?
- How do you design the best soup can?
- How large of an object can you carry about the corner?
- How short of a ladder will clear the fence?

## Applets

Below you will find a few applets that are useful for visualizing calculus concepts.

- Secant line of a graph (GeoGebra)
- Average rage of change (GeoGebra)
- Definition of the derivative as the limit of the slopes of secant lines (Desmos)
- Definition of the derivative as the limit of the slopes of secant lines (GeoGebra)
- Relationship between a graph and its derivative (GeoGebra)
- Slope and Derivative of a Function (GeoGebra)

## Reviews for Exams

To study for your exams, I recommend looking over and redoing as many homework problems as possible. This includes Daily and Weekly Homework. The correct answers for WeBWorK problems are always made available after an assignment’s due date. In addition, you should read over examples done in class and make sure you understand them. The review sheets posted below provide additional information about what sections and what topics you should be familiar with prior to each exam.

- Review for Exam 1 (
*Note:*You can skip problems 10 and 11 as we haven’t covered this yet.) - Review for Exam 2 (
*Note:*You can skip problems 2(h), 14(d) and 17 as we haven’t covered this yet.) - Review for Exam 3 (
*Note:*In addition, I suggest you do 2(h) and 17 from the previous review. However, you can skip problems 13-15 as we haven’t covered this yet. Also, I recommend doing additional problems involving logarithmic differentiation.) - Review for Exam 4 (
*Note:*You are also responsible for knowing how to solve related rates problems. In particular, check out problems 13-15 from Review for Exam 3)