Course Code & Number:
Level of Course:
Pre-requisites & Co-requisites:
Quiz - 5%
Homework - 10%
Exam 1 - 15%
Exam 2 - 15%
Exam 3 - 20%
Final - 35%
Vectors in Plane and 3-Space, Dot and Cross Products, Lines and Planes in Space. Vector-valued Functions and Their Limits, Derivatives and Continuity, Tangent Vectors and Arc Length, Curvature. Functions of Several Variables and Their Limits and Continuity, Partial Derivatives, Differentiability and Chain Rule, Gradients and Directional Derivatives, Tangent Planes, Maximum-Minimum Problems, Lagrange Multipliers. Double Integrals, Calculation of Volumes of Solids, Integrating in Polar Coordinates, Triple Integrals. Vector Fields, Line Integrals, Conservative Vector Fields and Path Independence, Divergence, Gradient and Curl, Green's Theorem, Surface Integrals, Stoke's Theorem, The Divergence Theorem.
Upon succesful completion of this course, a student will be able to
1. recall basic principles of mathematical writing, conventions, mathematical notation and fundamental definitions related to multivariable scalar and vector valued functions.
2. write equation of lines and planes in R^3.
3. extend the concepts of limit and continuity to multi-variable scalar and vector valued functions.
4. calculate limits, partial derivatives, directional derivatives, and multi-integrals of multi-variable scalar functions in various coordinate systems algebraically, graphically, and numerically.
5. compute limits, derivatives and curvature of vector valued functions algebraically, graphically and numerically.
6. solve problems of Maximum-Minimum Values and Lagrange Multipliers for multi-variable scalar functions.
7. calculate line integrals, divergence, gradient and curl of vector fields.
8. use main theorems of vector calculus such as Green’s Theorem, Stokes’s Theorem and Divergence Theorem.