Lehigh University

Math 23 Calculus III [4]

Instructor: Bruce Dodson

Current Course Catalog Description

Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; line integrals; Green’s Theorem, Gauss’s Theorem. Prerequisite: MATH 22 or MATH 32.

Textbook

J. Stewart, "Calculus, Early Transcendentals", 6th ed.

References

None

Course Outcomes

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. See below, Major Topics Covered in the Course.

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).

Major Topics Covered in the Course

Vectors and the Geometry of Space (dot product, cross product, lines and planes, cylinders and quadric surfaces, cylindrical and spherical coordinates).
Vector Functions and curves in space, arc length and curvature, motion.
Functions of Several Variables, Partial Derivatives and Applications (limits and continuity, tangent planes and linear approximation, the Chain Rule, directional derivatives and the gradient, extreme values, Lagrange Multipliers.
Double and Triple Integrals, including integrals in polar, cylindrical and spherical coordinates, others change of variables, applications, including moments and centers of mass, surface area.
Vector Calculus: line integrals and their fundamental theorem, Green's Theorem, curl and divergence, surface area and surface integrals, Stokes'Theorem, the Divergence Theorem (Gauss' Theorem).

Relationship between Course Outcomes and Program Outcomes

The MATH 23 outcomes strongly support the following outcome:

A. An ability to apply knowledge of computing and mathematics appropriate to the discipline.

Assessment Plan for the Course

The students take two midterms and a final examination. Homework is collected weekly and graded. There is also a quiz in recitation most weeks.

		Math 23 Calculus III [4] Instructor: Bruce Dodson Current Course Catalog Description Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; line integrals; Green’s Theorem, Gauss’s Theorem. Prerequisite: MATH 22 or MATH 32. Textbook J. Stewart, "Calculus, Early Transcendentals", 6th ed. References None Course Outcomes 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. See below, Major Topics Covered in the Course. 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). Major Topics Covered in the Course Vectors and the Geometry of Space (dot product, cross product, lines and planes, cylinders and quadric surfaces, cylindrical and spherical coordinates). Vector Functions and curves in space, arc length and curvature, motion. Functions of Several Variables, Partial Derivatives and Applications (limits and continuity, tangent planes and linear approximation, the Chain Rule, directional derivatives and the gradient, extreme values, Lagrange Multipliers. Double and Triple Integrals, including integrals in polar, cylindrical and spherical coordinates, others change of variables, applications, including moments and centers of mass, surface area. Vector Calculus: line integrals and their fundamental theorem, Green's Theorem, curl and divergence, surface area and surface integrals, Stokes'Theorem, the Divergence Theorem (Gauss' Theorem). Relationship between Course Outcomes and Program Outcomes The MATH 23 outcomes strongly support the following outcome: A. An ability to apply knowledge of computing and mathematics appropriate to the discipline. Assessment Plan for the Course The students take two midterms and a final examination. Homework is collected weekly and graded. There is also a quiz in recitation most weeks.