College in High School Course Syllabus
Math 0220
Analytic Geometry and Calculus 1
(4 CREDITS)
This course is the standard first course in a basic calculus sequence required for all mathematics, science, engineering, and statistics students.
The recommended text for this course is Calculus: Concepts & Contexts, third edition, by James Stewart (Thomson Publishing), but you may use any textbook as long as the material listed below is documented in the book.
Successful completion of high school algebra and trigonometry are prerequisites.
The following topics are covered:
Functions, limits, continuity, and derivatives
Derivative formulas
- Polynomials, products, quotients, Chain Rule, trigonometric functions, inverse functions, exponentials, logs, and inverse trigonometric functions
- Implicit differentiation
- Logarithmic differentiation
Tangent lines to curves, including those defined implicitly or parametrically
Motion
- Motion along a line: position, velocity, acceleration
- Parametric equations
- Newton's Laws
Application of Derivatives
- Differentials and linear approximation
- Newton's Method
- Graphing using the first and second derivative
- Horizontal and vertical asymptotes
- Optimization: The First and Second Derivative Tests; Applied optimization problems
- Related rates
- L'Hopital's Rule
Integration
- Riemann sums and the definite integral
- Area under a curve
- Formal properties: Additivity, linearity, triangle inequality
- The Fundamental Theorem
- Indefinite integrals: Recover a position from velocity, velocity from acceleration: Recover a function from its growth rate (derivative)
- Integration by substitution
- Intregration of powers of sines and cosines
- Integration by parts
- Integration of rational functions with linear or quadratic denominator