1. Review of Precalculus
a. unit Circle
b. trigonometric Identities
2. Limits & Continuity
a. defining limits
b. graphing limits
c. solving limits
d. limits approaching infinity
d. continuity & discontinuity
3. Derivatives
a. defining
b. graphing
c. second derivatives
4. Differentiation
a. power rule
b. product rule
c. quotient rule
d. exponential functions
e. chain rule
f. implicit differentiation
5. Uses of Derivatives
a. related rates
b. optimization
c. l’Hôpital’s Rule
6. Antiderivatives
a. area under curves
b. trapezoids
c. left endpoint rectangles
d. right endpoint rectangles
e. midpoint rectangles
7. Integration
a. indefinite integrals
b. fundamental theory of calculus
c. properties of integrals
d. u-substitution
e. differential equations
This is based off of Wesleyan University's Calculus 1 Syllabus. This website is based off of senior year Calculus at Science Leadership Academy, taught by Mr. Latimer. The fundamental idea of Calculus is to study change. The word itself comes from Latin meaning "small stone”. The main concept of Calculus is studying "instantaneous" change, which means studying change, but over tiny intervals of time. Calculus was invented by Newton in the 17th century. Newton also simultaneously discovered that the change of speed of objects could be modeled by simple laws of motion, in other words acceleration. There are two types of Calculus, differential and Integral. Differential Calculus is the mathematical way of cutting something into small pieces to find how it changes.