Roosevelt Academy Middelburg - Science

SCI 110 Elementary Calculus - Concepts & Connections

Content

Mathematics is one of the most challenging subjects to study and to apply in many different disciplines. The emphasis of this course is on understanding the underlying concepts, such that memorizing the formulas becomes easier. Secondly, the techniques discussed in this course are direclty applicable in fields such as biology, chemistry, economics, health & physiology, engineering, physics, and sports & entertainment. Hence, the subtitle Concepts & Connections. This course limits itself to real numbers; complex numbers are not discussed. The functions used in this course are polynomials, rational functions, and the exponential and logarithmic function; trigonometric functions are excluded from this course. Taking the derivative of a function is a very important tool in mathematics. This requires the concept of limits. Using this concept, we will derive a set of rules that allows for calculating any possible derivative of any possible function. Furthermore, the course discusses a number of important applications of differentiation, like optimization. The concept of functions will be expanded to incorporate functions of several variables. Partial derivatives, directional derivatives and the gradient will be introduced and used for constrained optimization problems. Another very important technique is integration of functions. Several techniques for integration will be discussed. Finally, matrix algebra and probability will be briefly discussed.