Calculus

Calculus – Application of Derivatives

by ComputingNotes
Book calculus by Thomas/Finney, 9th Edition, Page 189 Derivatives can be used to analyze the behaviour of functions and solve practical optimization problems. Max-Min Theorem relates to existence of max and min value for a function $f4$ that is continous at every point of closed interval I. Absoluted maxima and minima on a closed interval ... Read More

Calculus – Derivatives

by ComputingNotes
Book Calculus by Thomas/Finney, 9th Edition, Page 109 Derivates is one of the most important concept in calculus. It measures the rate at which a function changes. It is defined actually as the limit of secant slopes which is the slope of curve at a point. Derivative of the funtion $f$ with respect to variable ... Read More

Calculus – Limits and Continuity

by ComputingNotes
Book Calculus by Thomas/Finney, 9th Edition; Page 51 Limit: One of the main concept that differentiates calculus with algebra and trigonometry (page 51). Core concepts: limit, limits to describe how different functions changes or varies (continuously or erratically), how limits can be used to define tangent lines to the graph of the functions, derivative of ... Read More

Calculus – Trignometric Functions

by ComputingNotes
Book: Calculus by Thomas/Finney. 9th Edition Radian is a unit of measurment. In calculus, angle is measured in radian. (Navigation and astronomy uses degrees for angles) – page 35 Radian measure $\theta$ is given by $\frac{s}{r}$ wher $s$ is arc length AB and $r$ is the radius. Six basic trigonometric functions. Some other functions. For ... Read More

Calculus – Rate of Change and Limit

by ComputingNotes
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. Average rate of change of function $y=f(x)$ is given by ... Read More

Calculus – Functions

by ComputingNotes
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. y is called the function of x if, $y = ... Read More

Calculus – Coordinates, Lines and Increments

by ComputingNotes
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley. The coodinates of point $P(a,b)$ are $a$ and $b$. $a$ ... Read More

Calculus – Preliminaries

by ComputingNotes
Finney, R. L., Giordano, F. R., Weir, M. D., Thomas, G. B., Jr., & Calculus and analytic geometry. (2001). Thomas’ calculus (Tenth edition / based on the original work by George B. Thomas, Jr.,as revised by Ross L. Finney, Maurice D. Weir, and Frank R. Giordano.). Addison-Wesley.

Calculus – The Derivative

by ComputingNotes
Suppose function $latex y = f(x)$, then the derivative of the function can be denoted as: $latex f'(x), \frac{dy}{dx}, y’ or \frac{d}{dx}(f(x))$ BUT what does that mean actually? Derivative of a function? https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
error: