Calculus
Course #257
Credit 1.0
Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions of the numbers 0, π/6, π/4, π/3, π/2, and their multiples. This program of study includes properties of functions, limits, differential calculus, and integral calculus. Proper notation is stressed and is an important element when expressing written work. A graphing calculator is required for the course, as investigative techniques are an integral part of the complete understanding of the course.
Unit 1: Prerequisites for Calculus
This chapter reviews the most important things you need to know to start learning calculus. It al...
Unit 2: Limits and Continuity
The concept of a limit is one of the ideas that distinguish calculus from algebra and trigonometr...
Unit 3: Derivatives
In Unit 2, we learned how to find the slope of a tangent line to a curve as the limit of the slop...
Unit 4: Applications of Derivatives
In the past, when virtually all graphing was done by hand (often laboriously) derivatives were th...
Unit 5: The Definite Integral
The need to calculate instantaneous rates of change led the discoveries of calculus to an investi...
Unit 6: Differentiable Equations and Mathematical Modeling
One of the early accomplishments of calculus was predicting the future position of a planet from ...
Unit 7: Applications of Definite Integrals
At this point it should be apparent that finding the limits of Riemann sums is not just an intell...