MATH 208 2

WHY CALCULUS ? The History Of Calculus

Calculus in Engineering Civil Engineering For example, in hydraulic systems, basic fluid mechanics equations require calculus. Structural Engineering For example, structural analysis relating to seismic design requires calculus. Calculations of bearing capacity and shear strength of soil are done using calculus, as is the determination of lateral earth pressure and slope stability in complex situations. Electrical Engineering Computing voltages in electronic circuits requires the use of calculus differential equations

Mechanical engineering Many examples! Calculus is used for: Evaluating surface areas of complex objects Computing torques and forces Analyzing fluid flow in hydraulic systems … Aerospace Engineering For example, computing thrust of rockets that function in stages, modeling gravitational effects over time and space. Many other Engineering fields: Nuclear Engineering, Material Science, etc…

Calculus is everywhere! Calculus is also used in many more areas: Architecture Acoustics Politics Optics Music Sports Arts … Calculus is everywhere!

Class website: http://ougouag.com Contains ALL course material: Annoucements Syllabus Homework Assignments Lecture Notes MANY more resources…! Bookmark it!

Brightspace: brightspace.ccc.edu How do you log in? With your ccc credentials (login and password) DO it now! (on your tablet/phone…) Set up your profile to get my messages. I WILL BE USING BRIGHTSPACE TO POST ALL YOUR SCORES IN TESTS AND QUIZZES.

Syllabus Let’s go over it in detail. Please pay attention. I will be giving you a short quiz next time about its contents!

A couple more things…

Food in class (!) If you must eat, please choose items that are discreet and do not disturb class (no strong smells and crinkly noises!)

About you At the end of today’s session: turn in the handout I gave you. Fill in as much as is comfortable for you. All info will be appreciated and will help me to get to know you better. Let’s go around and mention our Name and Special thing 

Now let’s review a few things…

Several review links are posted on the class website! For example: PreCalculus Tutorials MATH2.org  Just Math Tutorials All of my Math 207!

Integrals review

Examples:

Answers:

Examples: 1. 3. 5. 2. 4. 6.

Answers: 1. 3. 5. 2. 4. 6.

The Definite Integral  

Net Area on interval [-1,9]? Total Area on interval [-1,9]?

Examples: 5. Find the NET area, then the TOTAL area between the curve y=x(x−3) and the x-axis over the interval [0 , 5] Extra - 6. Evaluate the shaded area

Answers: 5. Net area = A + B Total area = |A| + B        

Substitution Rule

Examples: Evaluate the following: Indefinite integral:  x3 cos(x4 + 2) dx Definite integral:

Answers: