Syllabus: Mastering Mathematics for Engineers: Calculus II: Multivariable functions
Index
This course is part of our Mastering Mathematics for Engineers program: a series of MOOCs to refresh and review your bachelor level mathematics. This is the first of two Calculus MOOCs - Calculus II.
In this course we focus on functions of several variables. In the first week you will learn how to approach and appreciate such functions, in weeks two trough four you will learn about differentiation and its applications and in weeks five and six you will learn how to integrate functions of two or three variables.
We use examples that are based on real-life applications and allow you to practice your mathematical skills in an engineering context.
Learning objectives
1. Visualize multivariable functions in various ways and interpret their formulas
2. Compute partial and directional derivatives and interpret the result
3. Obtain information about extremes by considering (partial) derivatives
4. Integrate functions of two and three variables using several integration techniques
5. Analyze challenging engineering problems using these techniques.
Course layout by week and topic
Week 1: Functions of several variables, their formulas, graphs and contour plots
Week 2: Partial differentiation, tangent lines and planes, chain rules for several variables, linearization for several variables
Week 3: Directional derivatives and gradients
Week 4: Extreme values, critical points, bounded and closed domains
Week 5: Integration of functions of two variables, type I and type II domains, polar coordinates
Week 6: Integration of functions of three variables, type 1, type 2 and type 3 domains, cylindrical coordinates, spherical coordinates
Resources and exercises (Grasple)
Before you start with the course activities and materials, it’s very important to get acquainted with the environment and in the Getting Started section you’ll find some introductory activities to get yourself prepared for this course; particularly pay attention to the section on how to use Grasple