Introduction to Calculus

The Precalculus module sets the scene by familiarizing students with key ideas and methodology, including the manipulation of equations, elementary functions, and the real number line. Students will also explore algebraic expressions, surds, and approximations, enabling a strong foundational understanding of precalculus.

The Functions module further builds on the precalculus foundation, introducing students to functions as rules, composite functions, inverse functions, and various types of functions, such as polynomial, power, exponential, logarithmic, and trigonometric functions. This module provides a comprehensive repertoire of functions and their applications.

The Introducing the Differential Calculus module delves into the methodology of slopes, average rates of change, tangents, secants, and different kinds of limits, leading to the understanding of derivatives and their applications. Students will also explore Leibniz notation, differentials, and practical applications of differentials.

The Properties and Applications of the Derivative module focuses on increasing and decreasing functions, sign diagrams, maxima, minima, concavity, inflections, curve sketching, and various differentiation rules and their applications. This module equips students with the essential tools for analyzing functions using differentiation.

The Introducing the Integral Calculus module covers inferring displacement from velocity, areas bounded by curves, Riemann sums, definite integrals, the Fundamental Theorem of Calculus, and applications of definite integrals. This module also explores the connection between areas and derivatives, integration by substitution, odd and even functions, and practical applications of the integral calculus.