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Calculus-Help added a new photo. How will you celebrate? Calculus has the reputation of being one of the most challenging subjects in school, even when compared with other advanced math classes.
Many calculus classes have specific pre-requisites, such as an understanding of advanced algebra, geometry, and trigonometry. A well-developed imagination will make it much easier to understand calculus. Since calculus works with physical, real-world concepts, the ability to visualize these things in your mind is crucial to your ability to understand and solve calculus problems.
You also need to learn how to attack problems from different angles. Even before you start your first day of calculus, you can work on improving your ability to learn and process advanced concepts. Structured dancing, such as tap and ballet, helps with convergent thinking—your ability to find a single, absolute answer to a problem.
On the other hand, more improvised styles of dance, like hip-hop or EDM dancing, improves divergent thinking. Since calculus requires both types of thinking, you should consider learning multiple styles of dance.
Many schools offer dance classes as an alternative to physical education, or as an elective. Over the last decade or two, there has been a rise in the popularity of logic and puzzle games like sudoku. Electronic games designed to work out your brain can be found on nearly any video game platform as well. Many logic or puzzle games require you to work a problem from multiple sides and have numerous ways of finding the solution.
Obviously, exercise and a proper diet will benefit your body; however, science also proves that a healthy body leads to a healthy mind. People who regularly work out and eat wholesome, healthy food, have more energy, which helps their brain work faster and harder. Researchers at Harvard found that regular cardio exercise can actually increase the size of your hippocampus, which is the part of the brain responsible for verbal memory and learning. A similar Harvard study also discovered a link between unhealthy food and memory problems.
They can help relieve stress for keeping focused on your work. REM sleep, in particular, is vital to your ability to form connections between unrelated ideas. While the above tips will prepare your brain to learn calculus, you may still need some extra help when it comes time to work through calculus exercises. If you find yourself struggling with a problem, try some of these tips.
A mind map is essentially a sketch of the problem and all the potential solutions. You can use this technique with any kind of question. Think of it as another way to brainstorm. By drawing out the issue, your mind may be stimulated to generate more ideas. Basically, you start with your problem in the center of the page.
As you brainstorm possible solutions, add branches off the center containing these answers. You can divide these main branches into sub-branches, as you plug in your potential answer to the problem and work through it.
Many studies have shown that the act of writing types of cement not only new ideas into your brain, but also generates new connections and creative ideas. The purpose of an idea journal is to provide a place for you to write out your problem and any subsequent ideas you generate over time. Keeping an idea journal with you at all times allows you to write out these solutions as soon as they pop into your head. For many people, the act of talking through a problem helps their mind sort through ideas and generate new solutions.
One common strategy is to talk through the problem as if you were teaching the subject to someone else. By explaining the concepts involved in the question to yourself or others , you could unlock the answers already hidden in your mind. As we mentioned earlier, most calculus problems can be represented physically—for instance, the shape of a curving slope, or the speed of a moving object. That allows your brain to think more abstractly and creatively on the issue at hand while your attention is focused somewhere else.
Focus on the parts of the problem that you already understand, and work through as much of it as you can. In the process of rehashing familiar concepts, you may trick your brain into forming the complete solution. Even more than mathematical ability, calculus requires creativity, adaptability, and excellent problem-solving skills.
If you work hard, take care of yourself, and use our guide to enhance your calculus capabilities with these brain-boosting tips, there should be nothing stopping you from earning that A.
Differential calculus looks at the instantaneous rate of change. So, what does that mean? A function is typically notated like this: For an equation to be a function, any number you plug in as the x variable has to cause the equation to equal precisely one value of y.
An independent variable is a value of x in a function. A dependent variable is whatever value is yielded by the function, represented in our example as y. The value of y will change depending on the value of x , the independent variable. The value of the independent variable always determines the value of a dependent variable.
The domain of an equation or function is a set of all the possible values of the independent variable x that will produce a valid dependent variable y. While the domain can be essentially infinite, for our purposes, we will create a relatively small domain. The ellipsis … indicates that all numbers in between 3 and 9 are included in the domain. The limit is the value that y approaches as x approaches a given value.
In our domain, 9 is the highest value x can be. So, the limit of our function is the value of y as x gets closer to 9. The process of finding the derivative of a function at any point is called differentiation, and differential calculus is the field that studies this process.
This overview of differential calculus introduces different concepts of the derivative and walks you through example problems. Integral calculus involves the concept of integration. Alongside differentiation, integration is one of the main operations in calculus. Integration is the process of finding the integral of a function at any point on a graph.
This lesson defines integration and also covers Riemann integration and the general power rule. Multivariable calculus, also called vector calculus, deals with functions of two variables in three- dimensional space. Multivariable calculus extends concepts found in differential and integral calculus.
Calculus has the reputation of being one of the most challenging subjects in school, even when compared with other advanced math classes. That’s because calculus is usually the first exposure students get to a version of math that requires more than just memorization to succeed.
Struggling with calculus? You're not alone. View our free calculus lessons and links to help ace your calculus class.
Flash Tutorials for the Calculus Phobe Chapter One: Limits and Continuity Lesson 1: What Is a Limit? Lesson 2: When Does a Limit Exist? Lesson 3: How do you evaluate limits? Lesson 4: Limits and Infinity Lesson 5: Continuity Lesson 6: The Intermediate Value Theorem Chapter Two: Finding Derivatives Lesson 1: The Difference Quotient . You can learn anything. Expert-created content and resources for every course and level. Always free.
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