A Survey of Calculus I

REQUIRED TEXTBOOKS AND COURSE MATERIALS

Textbook: This course will cover chapters 1-6 (omitting some sections) of the course text Applied Calculus for the Managerial, Life, and Social Sciences by Soo T. Tan, 9th edition (Publisher: Brooks/Cole Cengage Learning). Acquisition of a physical copy of the text is
optional. An electronic version of it is quite convenient though, since we will follow closedly the book.

Course materials: Additional material will be downloadable from UPV poliformaT platform after enrollment. A non-programmable scientific calculator is required.

DESCRIPTION

Math 1210 is an introductory calculus course intended for students interested primarily in the life, managerial, and social sciences. Calculus might be defined as a mathematical toolkit for analyzing functions. In virtually every area of human endeavor, functions are or
can be used to further understanding and to assist in making predictions.

• A biologist might be interested in population as a function of time.
• A medical researcher might be interested in modeling blood pressure as a function of body weight, or concentration of a drug in the bloodstream as a function of time since ingestion.
• A business executive might study the demand for a product as a function of its price, or, perhaps, as a function of the amount spent on marketing.
• An environmental scientist might be interested in the level of a toxin in a lake as a function of time.
• A physicist might be interested in the position of a moving object as a function of time.
• An astronomer might be interested in star luminosity as a function of mass.
• A chemist might be interested in solution concentration as a function of time. Calculus provides two fundamental tools for analyzing functions: the derivative, which represents the rate of change of a function, and the definite integral, which can be used to
compute the net change of a function over an interval. Derivatives and definite integrals are defined using the notion of limit, which is another tool of calculus. This course introduces you to the tools of calculus and their applications.

LEARNING GOALS

Upon successful completion of this course, students will 
• be able to work confidently with functions represented verbally, numerically (by a table of values), graphically, or algebraically (by a formula) and be able to relate, as well as create, such representations;
• understand, be able to describe, and be able to apply the fundamental tools that calculus provides for analyzing functions: derivatives, which represent rates of change,and definite integrals, which can be used to compute net change;
• recognize when the tools of calculus can be applied to analyze a function and be able to communicate —with clarity and precision— the results of their analysis;
• by modeling and solving a variety of problems including some with real-world applications, students will develop problem-solving skills and strategies such as breaking complex problems into simples subproblems and testing solutions for plausibility. They
will also come to understand how theoretical results and concepts can be developed and then used as tools for problem solving as well as further investigation;
• be able to assess the quality of competing solutions to problems based on criteria such as clarity, efficiency, and elegance.

PROGRAM CONTEXT

We will cover the following chapter of the course text:
1. Preliminaries
2. Functions, Limits, and derivative
3. Differentiation, skipping 3.4 and 3.7
4. Applications of the Derivative
5. Exponential and Logarithm Functions (skipping 5.3)
6. Integration, through 6.5.