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Biographical Sketch – Coach Jeff Durnford
I began teaching in Alief ISD in 1992 at Elsik High School. Prior to my arrival in Alief ISD, I served twelve years as a commissioned officer in the United States Army with assignments at Fort Bragg, North Carolina, Fort Huachuca, Arizona, the Republic of Korea, and the United States Military Academy. I moved to Taylor High School when the school opened in 2001. Since that time, I have taught mathematics and served as the Head Boy's Basketball Coach.
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Welcome to Alief Taylor Home Page
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Calculus is, simply stated, the study of change. The course begins with a study of the concept of a limit - how functions behave as the inputs approach a specific value or infinity. We use this foundation to study both differential calculus and integral calculus. We introduce differential calculus with a fundamental question - how do we measure the change in a function at a point? This discovery leads to the definition of the derivative and ultimately, to the rules which allow us to differentiate functions. Once we have established these concepts, the remainder of differential calculus explores curve analysis, optimization, related rates of change, and other applications of the derivative. Our study of integral calculus starts with an investigation of the area under a curve. From this basis, we develop the ideas of accumulation and the relationship between the derivative and the anti-derivative (indefinite integration). Following the development of integration techniques, we finish our study of integral calculus with applications of the integral - differential equations, area, and volume. This course concludes with a study of plane curves (polar curves, parametric curves, and vectors, infinite series, and Taylor polynomials. All students are expected to take the Advanced Placement Calculus BC exam in May.
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