1. Section 1.1 By: Thomas a.k.a. Taz Kostielney Thomas a.k.a. Roadrunner Krcmaric Chris a.k.a. Eagle Hoffman

2. What is Calculus? The mathematics of change, such as velocities and accelerations. Calculus allows people to model real life situations.

3. Calculus Basics There are two types of calculus: differential, the rate of change of something, and integral, which, among other things, is used to find the area under a curve.

4. When you do not need to use Calculus …when finding: –The slope of a line –Secant line to a curve –Curve of a circle –Height of a curve at a specific point –Tangent plane to a sphere –Direction of motion on a straight line –Average rate of change between two points

5. When you do not need to use Calculus –Finding the area of a rectangle –Work done by a constant force –Finding the center of a rectangle –Length of a line segment –Volume of a rectangular solid –Sum of a finite number of terms –Surface area of a cylinder

6. When you need Calculus …when finding: –Slope of a curve –Tangent line to a curve or surface –Instantaneous rate of change at a particular time –Curvature of a curve –Maximum height of a curve on an interval –Direction of motion on a curve

7. When you need Calculus –Area under a curve –Work done by a variable force –Length of an arc –Surface area of a solid of revolution –Mass of a solid with variable density –Volume of a region under a surface –Sum of an infinite number of terms

8. Tangent Line Problem Limits are a fundamental part of Calculus. You will be given a function and a point (c, f(c)) on that function. You want to find the tangent line at that particular point. Draw a secant line through the given point and another point (c+Δx, f(c+Δx)) on the curve.

9. Tangent Line Problem The slope of the tangent line is the limit of the slope of the secant line. (Don’t worry, this will all make sense to you when you actually do this.) –Slope of the secant = (Doesn’t that look pretty) –Slope of the tangent =

10. The Area Problem To find the area of a region under a curve, you place rectangles on the curve to the x-axis. Adding the rectangles’ areas approximates the overall area. The more rectangles, the more accurate the approximation. Apply a limit as the number of rectangles approaches infinity.

11. THE END…..