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Math 23 Calculus III [4]
Instructor: S. Szczepanski
Current Course Catalog Description
Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; line integrals; Green’s Theorem, Gauss’s Theorem.
Textbook
J. Stewart, Calculus, Early Transcendentals, 4th ed.
References
Course Goals
Students should master the concepts and techniques of multivariable calculus, including the geometry of vectors and curves in the plane and in space, functions of several variables, partial derivatives, continuity and differentiability of functions of several variables, the gradient and its significance, local, constrained and unconstrained extrema, multiple integrals, line integrals, exactness and path independence, Green’s Theorem, surface integrals, Stokes’s Theorem and Gauss’s Theorem.
Prerequisites by Topic
mastery of the concepts and techniques of single variable calculus as developed in Mathematics 21 and 22 (see course descriptions for Mathematics 21 and 22 and also their Annotated Syllabus Outlines, appended).
Major Topics Covered in the Course
See above, Catalog Description and Course Goals; see also Annotated Syllabus Outline, appended.
Laboratory projects (specify number of weeks on each)
Estimate CSAB Category Content
Data Structures
Every student is required to submit at least _____ written reports (not including exams, tests, quizzes, or commented programs) of typically _____ pages and to make _____ oral presentations of typically _____ minutes duration. Include only material that is graded for grammar, spelling, style, and so forth, as well as for technical content, completeness, and accuracy.
Social and Ethical Issues
Theoretical Content
vectors and curves in the plane and in space, functions of several variables, partial derivatives, continuity and differentiability of functions of several variables, the gradient and its significance, local, constrained and unconstrained extrema, multiple integrals, line integrals, exactness and path independence, Green’s Theorem, surface integrals, Stokes’s Theorem and Gauss’s Theorem. Somewhere between 60 to 70% of lecture time is devoted to these topics.
Problem Analysis
Identification of problem types and matching of techniques mastered to problem types.
Solution Design
Devising and carrying out solution strategies to problems from within Mathematics and from a wide range of applications areas. |
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