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In this course, you will :
- Explore the functions of various variables and learn what they're good for.
- Learn how to use a 3D image to capture the most important aspects of a function.
- Improve your ability to visualise the shape of a function and to think in three dimensions.
- Begin unravelling the mysteries of limits by searching for a mythical beast.
- Learn to visualise and apply limits in the real world.
- Discover the applications of a derivative's derivative, such as the wave equation.
- Learn how functions can achieve extreme values on unusual shapes.
- Create a simple test to classify local extrema using the microscope.
Syllabus :
1. Introduction
- Many Variables in a Nutshell
- Finding Extrema
- Coordinates in 3D
- 3D Volumes
2. Vector Bootcamp
- Vector Arithmetic
- Vector Properties
- Equations of Lines
- Dot Product Definition and Properties
3. Multivariable Functions
- Multivariable Functions
- Function Domains
- Basic Graphing
- Graphs by Slices
4. Limits with Many Variables
- Searching Square Lake
- Multivariable Limits
- Shock Waves and Discontinuities
5. Derivatives
- Basic Partial Derivatives
- Higher-Order Partials
- Under the Microscope: Tangent Planes
- Directional Derivatives
6. Optimization
- Local Maxima and Minima
- Back Under the Microscope: Quadrics
- Back Under the Microscope: Hessian Test
- Boundary Extrema
7. Multiple Integrals
- Double Integrals
- Fubini's Theorem
