UM52A: Multivariable Differential Calculus Syllabus

UM52A: Multivariable Differential Calculus
Syllabus
Course Description
Multivariable Differential Calculus is a one-semester course on differential
calculus of several variables. Particular emphasis is placed on integrated
problem-solving and proof-writing.
Learning Objectives
Upon successful completion of the Multivariable Differential Calculus course,
students will
• Be able to work with and analyze functions of several variables
represented in a variety of ways, including graphical, analytical,
numerical, and verbal.
• Be able to work with vector-valued functions, including the unit tangent,
normal, and binormal vectors.
• Understand the meaning of partial differentiation.
• Understand the chain rule for functions of two or more variables.
• Be able to work with common applications of partial differentiation such
as tangent planes and maximum/minimum problems with and without
constraints.
• Be able to communicate mathematics verbally and develop mathematical
models for applications of mathematics to physical situations.
• Be able to use technology to assist in mathematical problem-solving.
Required Textbook
Calculus, Late Transcendentals Combined
Howard Anton, Irl C. Bivens, and Stephen Davis
Printed textbook or eBook, WileyPLUS access code required

Course Topics
• Unit 1: Three-Dimensional Space and Vectors
Rectangular coordinates in 3-space; Spheres; Cylindrical surfaces;
Vectors; Dot product; Projections; Cross product; Parametric equations of
lines; Planes in 3-space; Quadric surfaces; Cylindrical and spherical
coordinates
• Unit 2: Vector-Valued Functions
Calculus of vector-valued functions; Change of parameter; Arc length;
Unit tangent, normal, and binormal vectors; Curvature; Motion along a
curve
• Unit 3: Partial Derivatives
Functions of two or more variables; Limits and continuity; Partial
derivatives; Differentiability, differentials, and local linearity; The chain
rule; Directional derivatives and gradients; Tangent planes and normal
vectors; Maxima and minimia of functions of two variables; Lagrange
multipliers
Overview of Assignments
Each semester, the letter grade in the course will be determined based on
performance on the following types of assignments.
• In class participation: Students are expected to participate in in-class
discussion sections, and are expected to have a functioning graphics tablet
for presenting problems and asking questions during discussion sections.
Students will contribute to and be part of an active learning environment.
• Homework assignments: Students will complete regular homework
assignments (written and/or electronic) to demonstrate their mastery and
knowledge of the material covered in each week’s lectures and discussion
sections.
• Unit exams: Students will complete written exams designed to test depth
of understanding of multivariable calculus concepts and the ability to
integrate knowledge of course concepts to solve problems and write
proofs. There will be approximately 2-3 such exams per semester.
• Final exam: There will be a comprehensive, proctored final exam each
semester. The final exam will include material covered in lecture,
discussion, homework assignments, and exams.