About This Chapter
Below is a sample breakdown of the Multi-Variable Calculus chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Piecewise functions||Domains, examples and applications of piecewise functions, translations of the graphs of piecewise functions|
|Tuesday||Composite functions||Methods for writing and evaluating composite functions, rules for manipulating functions|
|Wednesday||Lagrange multipliers||Extrema of multivariate functions, function optimization, constraints|
|Thursday||Partial derivatives||Problem-solving methods for partial differential equations|
|Friday||Constrained optimization||Steps for maximizing and minimizing functions, uses of partial derivatives|
1. What are Piecewise Functions?
A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.
2. Translating Piecewise Functions
Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.
3. How to Evaluate Composite Functions
Sometimes a math function depends on the outcome of another function. This lesson breaks down this chain reaction, called a composite function, and how to evaluate them.
4. Manipulating Functions and Solving Equations for Different Variables
Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.
5. Lagrange Multipliers Method & Examples
Finding extreme values like minimum distance and maximum area with calculus is fun. This lesson explores the Lagrange multiplier method which extends the calculus approach even further.
6. Solving Partial Derivative Equations
In this lesson, we'll introduce partial derivative equations and look into how they are solved. We'll explore several of the derivative rules and apply those rules to solve a few examples.
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Other chapters within the Business Calculus Syllabus & Lesson Plans course
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