Calculus I is where mathematics really starts to get interesting because its focus is on being able to describe the real, dynamic systems we see in real life that change over space and time. As such, this class will have a significant project-based component that will allow students to see the actual application of the techniques of differentiation and integration.
It starts with an introduction to limits. Finding limits helps in finding values that might not exist themselves but can be inferred by taking closer and closer approximations of reality.
We next use our knowledge of limits to derive the basic rules of differentiation: the power rule, basic trigonometric rules, product rule, quotient rule, chain rule and the rules implicit differentiation.
These rules are then used to in problem solving using differentiation. Mathematical problems include finding maximum, minimum and inflection points on curves, while computing the motion of projectiles (position, speed, acceleration) is particularly tractable when using differential calculus.
After differentiation we must necessarily study its inverse, integration. Using our knowledge of limits, we determine the basic rules of integration, then go into more complex rules. This will include an introduction to numerical techniques.
Our knowledge of integration is then applied to solving initial-value problems and other mathematical and real-life problems.
- Exams: 60%
- Projects: 40%
- Straight Lines/Linear Equations - draw straight lines from two points, or from equations in slope/intercept and point/slope forms (About).
- Parabolas - draw parabolas from standard and vertex form equations (About).
- Euler's Method - a numerical approach to solving differential equations (About).
- Numerical Integration Demo
- Slope Fields Demo
- Water lab report detailed outline.