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

CORE     ADVANCED 

Data Structures
Computer Organization and Architecture
Algorithms Software Design
Concepts of Programming Languages
 
 
Oral and Written Communications

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.