The Various Freshman and Sophomore Calculus Courses
This is the homepage for the Calculus offerings at Penn State University-University Park location. The engineering-science calculus sequence begins with Math 140 (4 credits), followed by Math 141 (4 credits), which, together, cover one variable differential and integral calculus and an introduction to sequences and series.
This sequence continues with Math 230 (4 credits), Several Variable Calculus. This course is also offered in two separate courses, Math 231 (2 credits) and Math 232 (credits) which cover the differential and integral calculus of several variables respectively. Finally, the sequence concludes with Math 250 (3 credits), Differential Equations, which also is offered in a slight expanded version covering some partial differential equations, Math 251 (4 credits).
Many students in this sequence also schedule Math 220 (2 credits) which covers basic linear algebra.
The business calculus sequence begins with Math 110 (4 credits). This course covers the basics of one-variable differential and integral calculus with applications to business. The second course, Math 111 (2 credits), is an introduction ot the calculus of several variables.
What is Calculus?
The remarkable progress that has been made in science and technology during the last century (especially the last decades) is due in large part to the development of mathematics. The branch of mathematics known as calculus serves as a natural and powerful tool for attacking a variety of problems that arise in physics, astronomy, engineering, chemistry, geology, biology, and other fields including, rather recently, some of the social sciences.
Why was polio eradicated by vaccination, but not measles? With what speed should a rocket be fired upward so that it never returns to earth? If a Vermeer (1632-1675) picture contains 99.5% of its carbon-14, can you determine whether the picture is a fake? It is reported that the Great pyramid of Egypt was built in 20 years. If the stone making up the pyramid has density 200 pounds per cubic foot, find the total amount of work done in building the pyramid and estimate how many workers were needed to build the pyramid? To model a conflict between two guerrilla armies, we assume that the rate that each one is put out of action is proportional to the product of the strengths of the two armies. Which side wins? What is a sustainable harvest level for Sei Whales? These examples, chosen from various fields, illustrate some of the technical questions that can be answered by routine applications of calculus.
But calculus is more than a technical tool—it is a collection of fascinating and exciting ideas that have interested thinking people for centuries. Many people consider calculus to be one of the greatest achievements of the human intellect. Inspired by problems in mechanics, Newton and Leibniz developed the ideas of calculus about 300 years ago. These concepts have to do with speed, area, volume, rate of growth, continuity, tangent line, and other concepts from a variety of fields. Calculus forces us to stop and think carefully about the meanings of the concepts. Another remarkable feature of the subject it its unifying power. Most of these ideas can be formulated so that they revolve around just two problems of a geometric nature.
Various Links for the Curious Calculus Student
- D. Arnold's Graphics for the Calculus Classroom (great!)
- Newton's Method (nice pictures)
- Math Archives: Calculus Resources Online
- The Rise of Calculus
- Short Biographies of Mathematicians of the Seventeenth and Eighteenth Centuries (Descartes, Pascal, Fermat, Newton, Leibniz, Euler, etc.)