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Ideal for High School and College Level Curriculums


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Suggested Topics
  • Coordinates, Graphs and Lines
  • Functions and Limits
  • Differentiation
  • Applications of Differentiation
  • Integration
  • Applications of the Definite Integral
  • Logarithm and Exponential Functions
  • Inverse Trigonometric and Hyperbolic Functions
  • Techniques of Integration
  • Improper Integrals: L'Hopital's Rule
  • Infinite Series
  • Topics in Analytical Geometry
  • Polar Coordinates and Parametric Equations
  • Three-Dimensional Space: Vectors
  • Vector-Valued Functions
  • Partial Derivatives
  • Multiple Integrals
  • Topics in Vector Calculus
  • Second Order Differential Equations

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What is Calculus

Calculus is the study of Rates of Change. Calculus as we know it today was developed in the later half of the seventeenth century by two mathematicians, Gottfried Leibniz and Isaac Newton. There are two main branches of calculus: Differential Calculus and Integral Calculus. Differential calculus determines the rate of change of a quantity; integral calculus finds the quantity where the rate of change is known. Functions are defined by a formula. It may be well you effort to read Common Algebraic and Calculus Errors for some helpful information.

Differential calculus describes the methods by which, given a function, you can find its associated rate of change function, called the derivative. The function must describe a constantly changing system, such as the temperature variation over the course of the day or the velocity of a planet around a star over the course of one rotation. The derivative of those functions would give you the rate that the temperature changed and the acceleration of the planet, respectively.

Integral calculus is like the opposite of differential calculus. Given the rate of change in a system, you can find the given values that describe the system's input. In other words, given the derivative, like acceleration, you can use integration to find the original function, like velocity. Also, you use integration to calculate values such as the area under a curve, the surface area, or the volume of a solid. Again, this is possible since you begin by approximating an area with a series of rectangles, and make your guess more and more accurate by studying the limit. The limit, or the number toward which the approximations tend, will give you the precise surface area.

About this page

On the left, under the Suggested Topics is a list of topics typically found in most college or university level Calculus curriculums. The list is provided to help you determine where you may need tutoring. Your particular topic may not be listed, but that does not imply that tutoring is unavailable. Just contact me and inquire if I can offer tutoring for your particular needs. I will promptly respond and you can decide what further action is required.

I have numerous texts on this subject and I am confident that whatever difficulties you are having in Calculus, I can be of assistance. I wish you the best of luck in your academic success and look forward to any inquiry you may send on how I may be able to help you.

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