Calculus

Third Draft - Updated 10/20/00

Prerequisite: Trig and Pre Calculus

First semester of this course focuses on the study of functions and their graphs. Polynomial, rational, exponential, logarithmic and trigonometric functions are covered. Second semester focuses on analytic trigonometry, vectors, matrices, determinants, systems of equations and inequalities, sequences, probability, statistics and analytic geometry.

1. The student understands and applies the concepts and procedures of mathematics.

• 1. evaluates limits including algebraic calculations and estimating from graphs or data
• 2. compares relative magnitudes of functions and their rates of change, exponential, polynomial, and logarithmic growth
• 3. geometric understanding of graphs of continuous functions
• 4. understands the concepts of derivatives when presented geometrically, numerically, and analytically
• 5. uses the trigonometric functions, modes, and their graphs.

2. The student uses mathematics to define and solve problems.

• 1. finds specific antiderivatives using initial conditions including applications to motion along a line
• 2. solves separable differential equations and uses them in modeling
• 3. adapts a variety of knowledge and techniques to solve other similar application problems
• 4. uses a graphing utility to solve complex problems
• 5. analyzes curves including the notions of monotonicity and concavity

3. The student uses mathematical reasoning

• 1. uses the Fundamental Theorem to evaluate definite integrals, represent a particular antiderivative, and the analytical and graphical analysis of functions
• 2. uses calculus to predict and explain the observed local and global behavior of a function
• 3. interprets derivatives as an instantaneous rate of change
• 4. knowledge of derivatives of basic functions, including exponential, logarithmic, trigonometric, and inverse trigonometric functions
• 5. supports arguments and justifies results using inductive and deductive reasoning
• 6. shows all steps when problem solving.

4. The student communicates knowledge and understanding in both everyday and mathematical language.

• 1. describes asymptotic behaviors in terms of limits involving infinity
• 2. uses implicit differentiation to find the derivative of an inverse function
• 3. expresses complex ideas and situations using mathematical language and notation in appropriate and efficient forms
• 4. organizes ideas and solutions in mathematical language that is appropriate for expressing conclusions

5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

• 1. interpretation of the derivatives as a rate of change in varied applied contexts, including velocity, speed, and acceleration
• 2. applies appropriate integrals in a variety of applications to model physical, social, or economic situations
• 3. applies mathematical thinking and modeling in other subject areas and real-life situations