Peter J. Littig
B CUSP 124
Develops modern calculus by investigating the questions, problems, and ideas that motivated its discovery and practice. Studies the real number system and functions defined on it, focusing on limits, area and tangent calculations, properties and applications of the derivative, and the notion of continuity. Emphasizes problem-solving and mathematical thinking. Prerequisite: minimum grade of 2.5 in B CUSP 123 or sufficient score on approved mathematics assessment test. Offered: AWSp.
This course, the first part of a two-quarter sequence, develops the modern calculus by investigating the questions, problems, and ideas that motivated its discovery and practice. We will begin with two questions posed by the philosophers of ancient Greece: What is the area of a planar figure? How can one find the line tangent to a point on a curve? These and related questions occupied the creative attention of mathematicians for two millennia. In one form or another, they will occupy our creative attention for the duration of this course.
In order to answer these questions, we will study the real number system and the properties of functions defined on it. In particular, we will explore the notions of continuity and differentiability, the theory of limits, and the problem of optimization. Each concept will be studied as it first appeared in scientific and mathematical discourse, and as it now appears in contemporary applications. A highlight of the course will be the study and complete solution of the Brachistochrone Problem. Rigorous mathematical thinking and problem-solving skills will be emphasized throughout.
Learning Goals and Objectives
During this course, students will be expected to: 1) Identify the major conceptual and theoretical themes of Calculus; 2) Solve mathematical problems of both contemporary and historical importance by applying the techniques learned in the course; 3) Describe the contributions made be various mathematicians and philosophers to the development of Calculus, including Archimedes, Descartes, Fermat, Pascal, Barrow, Roberval, Newton, and Leibniz. 4) Employ calculator- and computer-based technologies in solving computation-intensive problems; 5) Develop the skills required to write and communicate mathematical ideas.
Student learning goals
General method of instruction
I will strive for a balance between interactive lecturing and small group work.
This course will be challenging. As a result, it will be both exciting and rewarding. Calculus rests on a foundation of arithmetic, algebra, and geometry. As such, facility with arithmetic and algebraic manipulations is essential. Also, familiarity with polynomials, rational functions, trigonometric functions, and the conic sections will be helpful. Please contact me if you would like to discuss these topics further.
Class assignments and grading
Course assignments will include written problem sets and worksheets. The assignments will call upon you to think critically, to develop facility with mathematical methods and techniques, and to write clearly and effectively. You can expect an average of 12-15 hours of out-of-class work each week.
Your grade will be based on your performance on quizzes, the midterm, and the final exam, and the quality of your written work.