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Learn Multivariable Calculus Online


This course delves into the realm of differentiating functions of multiple variables and their practical applications. By the end of this course, you will deeply understand vectors, equations governing lines, planes, and quadratic surfaces, and willl also be able to navigate the terrain of double integrals and their many real-world applications.

Course Highlights:
  • Vectors
  • Equations of lines and planes
  • Unit Tangent and Principal normal vector of a 3D curve (Arclength)
  • Limits of functions of several variables at a point (Continuity)
  • Partial derivatives of functions of several variables
  • Gradient of a function (Directional derivatives)
  • Tangent plane of a surface at a given point
  • Differentials
  • Local and global extrema of functions of several variables
  • Lagrange multipliers
  • Double and Triple integrals
Course Benefits:
  • Perform vector operations and interpret them geometrically for a plane and 3D vectors
  • Given geometric constraints find the equations of lines and planes
  • Calculate the arclength while finding the tangent and normal vector of a 3D curve given parametrically
  • Find the limit of a function of several variables at a point and analyze its continuity
  • Find and interpret the mean of the partial derivative of a given function of several variables
  • Find the gradient of a function and apply it to calculate directional derivatives
  • Write the equation of a tangent plane of a surface at a given point
  • Check differentiability of a function of several variables and apply differentials for approximations
  • Find critical points of a function of several variables and test them for the local extrema and saddle points
  • Use Lagrange multipliers to solve optimization problems involving constraints
  • Calculate double integrals using Fubini’s theorem
  • Calculate triple intergrals and change coordinates
Transferring UC San Diego Division of Extended Studies Credit

Many UC San Diego Extended Studies may qualify for college credit to UC San Diego or other colleges or universities. The transfer of credit is determined solely by the receiving institution. Please discuss how your individual courses will transfer with the registrar's office at the receiving institution before you enroll.

Course Typically Offered: Online every quarter.  

Live discussion sessions will be held once a week. Attendance in these sessions is optional and the sessions will be recorded for students to view later. Exams will be given online during a set date and time.

Prerequisites:  Calculus II or knowledge in differentiation and Integration of functions of one variable, Trigonometry, or equivalent knowledge.

More Information: For more information about this course contact

Course Number: MATH-40025
Credit: 4.00 unit(s)

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