DelftX: Calculus II: Multivariable Functions

• Visualize functions of two variables and read off qualitative information from graphs and contour plots.
• Calculate (higher order) partial derivatives for a variety of multivariable functions.
• Calculate and interpret directional derivatives and gradients of multivariable functions.
• Find and classify critical points of functions of two variables and determine extreme values for functions of compact domains.
• Evaluate double integrals over general integration domains using cartesian or polar coordinates.
• Evaluate triple integrals over general integration domains using cartesian, cylindrical or spherical coordinates.

Week 1:

• multivariable functions
• graphs of functions of two variables
• contour plots

Week 2:

• partial derivatives
• tangent planes and linearizations
• higher order partial derivatives
• chain rule

Week 3:

• directional derivatives and gradients
• maximizing directional derivatives
• applications of gradients

Week 4:

• extreme values
• critical points
• finding extreme values

Week 5:

• double integrals
• integrals over rectangles
• double integrals over general regions
• polar coordinates

Week 6:

• triple integrals
• triple integrals over general regions
• cylindrical coordinates
• spherical coordinates

Q: I am going to start a master’s in engineering. Is this MOOC mandatory?
A: It is not mandatory, but we believe it could be useful to revisit some of these topics.

Q: Can I use the certificate I get from this MOOC to get an exemption from a certain course?
A: No, you cannot. That is not the goal of these courses.

Q: Can I use this MOOC as a substitute for the Bridging Programme (Schakelprogramma)?
A: No, you cannot.

Q: What level is required to follow this course?
A: It is a review course. Hence the pace will be a bit higher than when you learn about these topics for the first time.

Q: What is the duration of this course?
A: You will probably need 4 to 6 hours per week, for 6 weeks.

Q: I am going to follow this MOOC. Will I have to hand in homework?
A: No. The exercises will be checked automatically, and you will get immediate feedback.