About This Chapter
Calculus: Min/Max & Integrals - Chapter Summary
In this chapter you will focus on analyzing lines in calculus. You will start by working with determining minimums and maximums. Then the instructors examine line integrals with the fundamental theorem of calculus. Finally, Green's theorem and gradient fields are discussed.
If calculus isn't exactly your favorite subject or it has just been a long time since you've even looked at a calculus book, these short lessons will help you brush up on some calculus basics. By reviewing these lessons and getting back up to ninja-level mathematical fitness, you'll easily take on the more complicated calculus functions in other chapters. This chapter will get you going again on:
- Using the Lagrange multiplier method and constraints to solve minimum and maximum problems
- Understanding line integrals and how to use the fundamental theorem of calculus to work with them
- Defining double integrals and evaluating them using iterated integrals
- Working with Green's theorem to evaluate closed double integrals
- Explaining gradient fields and their path independence
Each lesson is specially crafted by a professional mathematician with lots of experience to engage your attention and bring these mathematical principles to you in a fun manner. You will have the freedom to study at your own pace. The video lessons let you skip around to the parts you need with the handy video tags. Take the quizzes after each lesson to see how well you are understanding that material. Use the chapter quiz to gauge synthesis of the concepts or take it before beginning the chapter to focus your studies on those specific topics where you need the most practice.
1. Solving Min-Max Problems Using Derivatives
Max and min problems show up in our daily lives extremely often. In this lesson, we will look at how to use derivatives to find maxima and minima of functions, and in the process solve problems involving maxima and minima.
2. Line Integrals: How to Integrate Functions Over Paths
Many real-world functions are three dimensional, as we live in a 3D world. In this article, you will learn how to integrate 3D functions over general paths through space. This is a basic skill needed for real science and engineering applications.
3. The Fundamental Theorem of Calculus
The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.
4. Double Integrals & Evaluation by Iterated Integrals
In this lesson, we show how to evaluate a double integral using iterative integration. A special case is also presented which simplifies the calculations.
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Other chapters within the GRE Math: Study Guide & Test Prep course
- Functions in Precalculus
- Analytical Geometry in Precalculus
- Polynomial Equations in Precalculus
- Logarithms & Trigonometry
- Limits of Sequences & Functions
- Calculating Derivatives
- Curve Sketching in Precalculus
- Differentiable Functions & Min-Max Problems
- Indefinite Integrals in Calculus
- Definite Integrals in Calculus
- Additional Topics in Calculus
- L'Hopital's Rule, Integrals & Series in Calculus
- Analytic Geometry in 3-Dimensions
- Partial Derivatives
- Algebra: Differential Equations
- Algebra: Matrices & Vectors
- Algebra: Determinants & Transformations
- Algebra: Number Theory & Abstract Algebra
- Additional Topics: Sets
- Additional Topics: Unions & Intersections
- Additional Topics: Graphing & Probability
- Additional Topics: Standard Deviation
- Additional Topics: Topology & Complex Variables
- Additional Topics: Trigonometry
- Additional Topics: Theorems, Analysis & Optimizing
- GRE Math Flashcards