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:

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

## Course Outline

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

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