Special Functions in Mathematics

This module focuses on exponential functions and their properties in mathematics. Students will learn to establish and use the algebraic properties of exponential functions, recognize their qualitative features including asymptotes, and identify real-world contexts suitable for modeling with exponential functions. The module develops practical problem-solving skills using exponential functions in various applications such as growth and decay processes.

This module explores logarithmic functions and their relationship to exponential functions. Students will learn to recognize and use the inverse relationship between logarithms and exponentials, establish and use algebraic properties of logarithms, interpret logarithmic scales, recognize qualitative features of logarithmic graphs, and identify contexts suitable for modeling with logarithmic functions. The module develops skills in solving practical problems using logarithmic functions through algebraic, graphical, and technological approaches.

This module covers the fundamental concepts of trigonometric functions and their applications. Students will learn the unit circle definition of sine, cosine, and tangent using radians, recognize their graphical representations, describe amplitude, period, and phase changes, prove and apply common trigonometric identities, and identify contexts suitable for modeling with trigonometric functions. The module develops skills for solving practical problems involving periodic phenomena such as wave motion and oscillations.

This module examines reciprocal and absolute value functions and their properties. Students will learn to recognize the shapes of graphs for reciprocal functions and absolute value functions, apply the properties of absolute values to solve equations, and describe the effect of performing the absolute value operation on existing functions. The module develops understanding of these special functions and their applications in mathematical modeling.

This module consists of a timed exam designed to evaluate students' understanding of special functions covered throughout the course. The assessment tests knowledge of exponential functions, logarithmic functions, trigonometric functions, and reciprocal and absolute value functions. This comprehensive evaluation helps students gauge their mastery of these special functions and their applications to real-world problems.