{"id":1440,"date":"2023-02-15T12:01:59","date_gmt":"2023-02-15T20:01:59","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=1440"},"modified":"2023-08-22T16:04:36","modified_gmt":"2023-08-22T23:04:36","slug":"math-226-calculus-3","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-226-calculus-3\/","title":{"rendered":"MATH 226 – Calculus III"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

Math 226 is a coordinated course<\/a> and a common final exam is offered at the end of each semester.<\/span>
\nYou can find past common finals here<\/a>.<\/span><\/p>\n

 <\/p>\n

REQUIRED TEXTBOOK<\/strong><\/p>\n

Stewart, Essential Calculus (2nd ed.)<\/a><\/p>\n

 <\/p>\n

SECTION COVERAGE<\/strong><\/p>\n

The following table lists the minimum<\/em> set of topics to be included in this course.\u00a0 The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.<\/p>\n

There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.<\/p>\n\n\n\n\n\n\n\n\n
Sections<\/strong><\/td>\nTopics<\/strong><\/td>\nLectures<\/strong><\/td>\n<\/tr>\n
10.1 – 10.7<\/td>\nVectors and Geometry in R(3)<\/td>\n9<\/td>\n<\/tr>\n
11.1 – 11.8<\/td>\nPartial Derivatives<\/td>\n10<\/td>\n<\/tr>\n
12.1-1-12.7<\/td>\nMultiple Integrals<\/td>\n9<\/td>\n<\/tr>\n
13.1 – 13.9<\/td>\nVector Calculus<\/td>\n11<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n39<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

OPTIONAL TOPICS
\n<\/strong><\/p>\n

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

    If all<\/em> course instructors in a given semester cover a particular topic, they may choose to include that topic in the common final exam.<\/p>\n

     <\/p>\n

    MEASURABLE OBJECTIVES<\/strong><\/p>\n

    By the end of this course, students should be able to:<\/p>\n

     <\/p>\n

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

       <\/p>\n

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