Math 226 is a coordinated course and a common final exam is offered at the end of each semester.
You can find past common finals here.



Stewart, Essential Calculus (2nd ed.)



The following table lists the minimum set of topics to be included in this course.  The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.

There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.

Sections Topics Lectures
10.1 – 10.7 Vectors and Geometry in R(3) 9
11.1 – 11.8 Partial Derivatives 10
12.1-1-12.7 Multiple Integrals 9
13.1 – 13.9 Vector Calculus 11
Total 39


  • Section 10.8’s later elements of Differential Geometry, such as N and B.
  • Section 10.9 on Motion in Space and the Components of Acceleration.
  • In Section 12.4, students should understand the relationship between density and mass, but content on Moments of Mass and Inertia can be omitted.
  • Section 12.8 on General Changes of Variables.
  • Other outside topics, readings, videos, or materials the Instructor deems relevant.

If all course instructors in a given semester cover a particular topic, they may choose to include that topic in the common final exam.



By the end of this course, students should be able to:


  1. Understand and analyze three-dimensional space, vectors, and vector operations, including dot product, cross product, and projections.
  2. Determine and graph equations of lines, planes, and spheres in three dimensional coordinate systems, determine distances between points, lines and planes.
  3. Classify quadratic equations in three variables as representations of quadric surfaces.
  4. Identify and graph vectors functions, differentiate and integrate vectors functions, calculate arc length and curvature of space curves. Determine velocity and acceleration of space curves.
  5. Compute limits, partial derivatives, directional derivatives, and gradients for functions of several variables.
  6. Apply the chain rule for functions of multiple variables and partial derivatives to find derivatives of composite functions.
  7. Explore and graph surfaces, level curves, and level surfaces of functions of two or three variables.
  8. Optimize functions of two variables using second derivative test and extreme value theorem.
  9. Optimize multivariable functions with a constraint using Lagrange multipliers.
  10. Compute and interpret double and triple integrals over various regions, including those written in rectangular, polar, cylindrical, and spherical coordinates.
  11. Understand vector fields and their properties, including divergence and curl.
  12. Determine if a given vector field is conservative and find its potential function.
  13. Understand and apply line integrals with respect to arc length, work, and circulation, as well as conservative vector fields and potential functions.
  14. Apply the Fundamental Theorem for Line Integrals.
  15. Apply Green’s theorem to relate line integrals to double integrals over regions in the plane.
  16. Understand the concept of surface integrals and compute them over parametric surfaces and vector fields.
  17. Apply the divergence theorem to relate surface integrals to volume integrals and calculate flux across closed surfaces.
  18. Use Stokes’ theorem to relate surface integrals to line integrals and compute circulation and flux of vector fields.
  19. Solve real-world problems in physics, engineering, and other fields using concepts from multivariable calculus.
  20. Utilize computational tools and software (e.g., MATLAB, Mathematica, or Python) to perform multivariable calculus calculations and visualize three-dimensional objects and vector fields.