**MA161 CALCULUS I (4 Cr.)**

*Applies toward the division III liberal studies requirement.*

**MA163 CALCULUS II (4 Cr.)**

**COURSE DESCRIPTIONS**

Prerequisite: MA 115 or satisfactory score on the Math Placement Exam. A graphing calculator or equivalent software is required.

Offered: Fall, Winter

**General Introduction and Goals **

The Calculus sequence is offered in three semesters. (The course description for Calculus III (MA 265) is included separately.) This sequence of courses serves many majors, in addition to our own, and provides students with the opportunity to develop logical reasoning and complex problem-solving skills, and to learn useful applications.

Calculus is a pinnacle of intellectual achievement with a remarkable ability to express characteristic properties of natural phenomena. More importantly, calculus contains a wealth of computational tools that assist in analyzing these relationships. In fact, the computational tools are now so well understood that they can be reliably done in software. Accordingly, greater emphasis will be given in these courses to achieving a deeper understanding of the principles of calculus and the ability of students to apply these principles, with technological support, in a wide variety of settings.

In these courses, the student will have the opportunity

- to explore the fundamental paradigm of Calculus:
*approximate and find the limit of increasingly more precise approximations*; - to relate the fundamental paradigm to the characteristic applications in the physical and social sciences;
- to develop the capability of expressing natural phenomena using the concepts and notation of calculus;
- to develop an understanding of the inter-relationships between numerical, graphical and symbolic expressions of a problem;
- to build a good working set of computational capabilities and provide access to computer algebra systems, graphing calculators or similar technological support for non-routine, but well understood algorithmic processes;
- to learn to think conceptually, and to look at a problem both from the perspective of first principles as well as a member of a class of problems for which general techniques apply; and
- to develop expository writing skills of the form associated with a report.

*Note: no special emphasis is given to the role of technology in the description of the course content. That is not to be taken to mean that no such instruction will take place in these courses. On the contrary, it is assumed that graphing calculators, computer algebra systems, spread sheets and similar technological support will be included regularly throughout the courses.*

**Course Content **

**Calculus I**

- Functions
- Fundamental properties of algebraic, trigonometric and exponential functions.
- Phenomena modelled by functions including algebraic, trigonometric and exponential functions.

- Limits
- The Derivative
- The meaning of derivative
- Finding derivatives of functions given by table, by graph, and by formula
- Derivatives of the fundamental functions
- Derivatives of sums, products and compositions of functions
- Selected applications of the derivative
- Optimization
- Rate of change
- Linear approximation

- The Definite Integral
- The meaning of the definite integral
- Finding the definite integral of functions given by table, by graph and by formula
- The Fundamental Theorem of Calculus
- Selected applications of the definite integral
- Area under a curve
- Total change from rate of change

**Calculus II**

- The Integral
- Integration Techniques
- Tables
- By parts
- Substitution

- Applications
- Geometric
- In the physical and social sciences
- In probability

- Integration Techniques
- Sequences and Series
- Convergence
- Tests of convergence

- Approximation of functions
- Taylor's Series
- Fourier Series