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#### Calculus III: Multivariable Calculus

The main topic of this course is differentiation of functions of several variables and their applications. Vectors and the equations of lines, planes and quadratics surfaces will be discussed as well as double integrals and their 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 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

Course Typically Offered: Online during Spring and Summer quarters.
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.