Additional Online Case Studies & Appendices

#### Assessing Allegheny College’s introductory calculus and precalculus coursesAppendix B

Ronald Harrell and Tamara Lakins
Allegheny College
December 30, 2003

Appendix B:  Detailed course descriptions and learning goals.

Math 110 (Elementary Mathematical Models) is an algebra-based elementary modeling course intended for students who need a mathematics course but who do not need calculus.  Linear, polynomial, exponential, and logarithmic functions are studied.  The emphasis is on real-world problems and models, and rates of change.  Algebra is reviewed as needed.  Upon completing the course, the student will be able to

• work with functions and data represented graphically, numerically, analytically, and verbally;
• use technology appropriately in mathematical problem solving, and recognize its limitations;
• accurately perform algebraic manipulations; work with formulas;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.

Math 150 (Precalculus) is a traditional precalculus course intended solely for students who need extra preparation before attempting Math 160, the first course in the regular calculus sequence.  The mathematical concepts that are a prerequisite to the study of calculus (functions, domains, ranges, graphs, equations, and inequalities) are covered. Upon completing the course, the student will be able to

• manipulate algebraic expressions easily;
• work with polynomial and rational functions, including finding their values, graphing them, understanding their basic properties, and solving equations and inequalities;
• work with trigonometric functions, including finding their values, graphing them, using trigonometric identities, understanding their basic properties, solving equations, and solving problems in triangle trigonometry;
• work with exponential and logarithmic functions, including finding their values, graphing them, understanding their basic properties, and solving equations;
• communicate mathematical information in written form.

The courses Math 157/158 (Calculus I and II for Social/Life Sciences) form a two-semester terminal calculus sequence that gives primarily a conceptual treatment of calculus and is less theoretical than the regular calculus sequence.  The intended audience is economics, biology, and environmental science students.

Math 157 (Calculus I for Social/Life Sciences) is an introduction to the differential calculus of algebraic, logarithmic, and exponential functions.  The emphasis is on the concept of the derivative and its applications of calculus to the life and social sciences.  Precalculus topics are covered as needed.  Upon completing the course, the student will be able to

• work with functions and data represented graphically, numerically, analytically, and verbally;
• demonstrate an understanding of the concept of the limit of a function and the rules for showing the existence of and finding limits;
• demonstrate an understanding of the concept of the derivative of a function: the definition, as well its connection to the slope of  tangent lines and instantaneous rates;
• accurately perform the algebraic and calculus computations associated with algebraic, logarithmic, and exponential functions;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.

Math 158 (Calculus II for Social/Life Sciences) is a continuation of the differential calculus begun in Math 157, and an introduction to integral calculus of one variable and the differential calculus of multivariable functions involving algebraic, logarithmic, and exponential expressions. Applications of these topics in the life and social sciences are considered.  Upon completing the course, the student will be able to

• demonstrate how the derivative can be used to determine monotonicity, concavity, points of inflection, and maximums and minimums of functions;
• demonstrate an understanding of the definite integral as representing area and accumulated change, antiderivatives, and the Fundamental Theorem of Calculus;
• demonstrate familiarity with functions of several variables, partial differentiation and the information partial derivatives reveal about functions;
• accurately perform the algebraic and calculus computations with functions of several variables that involve algebraic, logarithmic, and exponential expressions;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.