CHARTER SCHOOL OF WILMINGTON COURSE OUTLINE CALCULUS 3
COURSE DESCRIPTION Students in Calculus 3 will continue their study of the calculus, particularly the calculus of space. Topics include using vectors to study shapes in two and three dimensions, vector-valued functions, functions of several variables, multiple integration and the solving of first and second order differential equations. Throughout the course real-world problems will be solved using the material learned. TEXTBOOK Calculus by Roland E. Larson, Robert P. Hostetler, and Bruce H. Edwards. D. C. Heath and Company, 1994 (5th edition). TEXTBOOK OUTLINE Chapter 9 Conic Sections
The purpose of this chapter is to aid the students is recognizing the general shape of the conic when given its general equation. The properties of conics and their applications will also be studied. Chapter 11 Vectors and the Geometry of Space
After introducing vectors in two dimensions, students will apply their knowledge to solve real-world applications using vectors. This study of vectors will then move to three dimensions. Using the previous material on conics, the student will study the properties various shapes in space. Chapter 12 Vector Valued Functions
Students will extend their knowledge of vector-valued functions and their applications in two and three dimensions.
M. Coté
1
Chapter 13
Functions of Several Variables
Students will explore shapes in space that can be generated with multivariable functions. They will learn the differential calculus that can be used with these shapes. And they will apply this calculus to solve applications. Chapter 14 Multiple Integration
Multiple integration and its applications will be studied in this chapter. It will be a natural extension to the calculus learned in the previous chapter to find volumes, surface areas, moments and centers of mass of objects. Cylinder and spherical coordinates will also be studied. Chapter 15 Vector Analysis
Properties of vector fields, line integrals, parametric surfaces, and their applications will be studied. Chapter 16 Differential Equations
The study of slope fields and the solving of simple differential equations by separation of variables will be extended. Students will learn to classify differential equations and some of the techniques for solving them. Once again, applications will be studied. TECHNOLOGY INCORPORATED IN THE COURSE The use of the TI-89 or TI-92 along with the software package, Maple, will be used to generate the shapes in three dimensions, solve the calculus set-ups, and prove some mathematical properties of the shapes.
M. Coté
2