ONLINE HIGH SCHOOL

UM52A:  Multivariable  Differential  Calculus  

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.