See the geometry
Graphs, level sets, gradients, tangent objects, and coordinate systems make multivariable formulas interpretable.
Worcester Polytechnic Institute · instructor of record
MA 1024: Calculus IV
An introduction to multivariable calculus, with emphasis on geometric interpretation and the extension of single-variable ideas to functions of several variables.
Course approach
This page consolidates representative materials across repeated offerings of the same course.
Differentiate and optimize
Partial derivatives and gradients are connected to local approximation and optimization.
Accumulate in higher dimensions
Double and triple integrals are framed as geometric and physical accumulation.
Representative course materials
The materials below use fixed filenames so the page remains unchanged when the PDFs are updated.
syllabus.pdf
Syllabus
Course structure, policies, learning objectives, grading, and schedule.
lecture_notes.pdf
Lecture notes
A representative set of notes, worked examples, and course development.
exam_1.pdf
Sample Exam 1
A representative earlier-course assessment.
exam_2.pdf
Sample Exam 2
A representative later-course assessment.