SYLLABUS - MATH 275 - CALCULUS III- Joel Cruz - F.pdf -...

Wenzheng College of Soochow University
MATH 275 – ANALYTIC GEOMETRY and CALCULUS III
Course Syllabus
SPRING 2017, 3 credit hours
Instructor: Joel Cruz
Class Meets: Tues – Frid 13:30 to 16:00 pm
Office: Room 101 Teaching Building #1
Email: [email protected]
General Course Objectives : :
This course is an introduction to the calculus of functions of several variables. It begins with studying the basic
objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces,
and various coordinate systems. It continues with the elementary differential geometry of vector functions and
space curves. By the end of the course, the student should be able to analyze curves and surfaces in three-space,
differentiate and determine any extrema of functions of two or more variables, evaluate double and triple
integrals in various coordinate systems
Course Description:
Rectangular, cylindrical and spherical coordinates. Vectors, lines, planes, cylinders, quadric surfaces.
Vector functions, curves, motion in space. Differential and integral calculus of several variables.
Vector fields, line integrals, fundamental theorem for line integrals, Green's theorem. Quantitative.
Required Text & Materials:
Textbook ：
Calculus Early Transcendentals,7th edition,by Edwards & Penny
Chapter 11 – Vectors and the Geometry of Space
Three Dimensional Coordinate System
Vectors
The Dot Product
The Cross Product
Equations of Lines and Planes
Cylinders and Quadric Surfaces
– Vector Functions
Vector Functions and Space Curves
Derivatives and Integrals of Vector Functions
Arc Length and Curvature
Motion in Space
Chapter 12 - Partial Derivatives
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers and Constrained Maximum

Chapter 13 – Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Triple Integrals
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates