MAT 397 is the third course in a three-semester sequence in calculus designed for mathematics, science, and engineering majors and those in other majors who intend to take advanced courses in mathematics.

Concepts covered in the course include: vectors, vector-valued functions, functions of several variables, partial derivatives, and multiple integration.

**Prerequisites**

To register for this course, students must provide documents confirming completion of one of the following prerequisites:

- Passing Syracuse University MAT 295 and 296 with a grade of C- or better;
- Earning a score of 4 or better on the AP BC calculus examination; or
- Earning a qualifying score on university examinations

**Course Outline**

- Definition and properties of the natural logarithm; definition and properties of the exponential function; the calculus of logs and exponentials.
- L’Hopital’s rule and indeterminate forms.
- Separable and linear differential equations with applications, especially growth and decay models.
- Definition and properties of inverse trigonometric functions and the calculus of these functions.
- Techniques of integration: review of substitution; completing the square; long division, etc.; integration by parts; integration of powers of trigonometric functions.
- Integration by partial fractions; integration by trigonometric substitutions.
- Improper integrals.
- Polar coordinates; areas in polar coordinates.
- Infinite sequences; convergence and divergence; the bounded monotonic sequence property.
- Infinite series; the geometric series; properties of series; the nth term test; the harmonic series.
- Taylor series and polynomials; Taylor’s formula with remainder; approximation; Maclaurin series.
- The integral test; comparison test; alternating series test; absolute convergence; the root test; the ratio test.
- Power series; radius of convergence; interval of convergence; differentiation and integration of power series.
- Approximations and computation using power series.
- Calculus of parametric curves.

A class set of graphing calculators is required (recommended: Texas Instruments TI-83 Plus or TI-84 Plus).