Develop an understanding of multivariate calculus, its structure, and applicability to functions and analytic geometry.
For information regarding prerequisites for this course, please refer to the Academic Course Catalog.
This course is an introduction to real multivariate calculus. After successful completion of this course the student should be able to calculate and explain all the major theorems and results of standard multivariable calculus.
Topics covered include the analysis of limits, continuity, differentiation, integration and power series for functions in one or more variables are developed. In addition, applications to optimization in several variables are discussed. The analytic geometry of curves and surfaces are analyzed with calculus. Integration of vector fields along curves and surfaces is developed and the major theorems of vector calculus are detailed and applied. This course of study should prepare both teachers and students for further study or instruction of multivariable calculus.
Measurable Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Define the limit using the epsilon delta formulation.
- Define differentiability of a map in terms of limits.
- State and apply the Fundamental Theorem of Calculus.
- Calculate partial derivatives and multiple
- Optimize functions of several variables either with or without
- State and apply the inverse and implicit function
- Calculate line and surface
- State and apply the major theorems of vector
- Calculate exterior derivatives and state the Generalized Stokes’ Theorem.
Textbook readings and lecture presentations
Course Requirements Checklist
After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in Module/Week 1.
Homework will cover the Reading & Study material for the assigned module(s)/week(s). Each homework is assigned through WebAssign, and the student will have 6 attempts for each problem. If the problem is incorrect 3 times, WebAssign will show you the correct answer and give you 3 attempts at a similar problem. Students are encouraged to work out their solutions on paper using correct mathematical notation before entering their answers into WebAssign. A score of 70% must be obtained in order to access the following assignment/quiz/test for that module/week.
Each quiz will cover the Reading & Study material for the assigned module(s)/week(s). Each quiz will be delivered within WebAssign, and they will be open-book/open-notes. Students are encouraged to work out their solutions on paper using correct mathematical notation before entering their answers into WebAssign. Students will have 3 attempts at each quiz.
Each test will have a time limit of 1 hour and 30 minutes. Tests will be open-book/open-notes, and will be delivered within WebAssign. Written work for the tests must be submitted in Blackboard immediately after completing the test in WebAssign and before the due date/time. Students will complete the WebAssign test AND submit a scan or picture of the written work in Blackboard before the due date/time. Tests submitted without accompanying written work will not be accepted. There will be only 1 attempt at each test.
Students will have 2 hours and 30 minutes to complete the Final Exam. The Final Exam is a cumulative exam delivered within WebAssign. This is an open-book/open-notes, timed test which must be completed in a single sitting. Written work for the Final Exam must be submitted in Blackboard immediately after completing the test in WebAssign and before the due date/time. Tests submitted without accompanying written work will not be accepted. There will be only 1 attempt for the Final Exam.