The course culminates in Applications of Derivatives — where students use calculus to solve real optimization problems, analyze function behavior, sketch curves, and tackle related rates challenges. With over 20 dedicated practice and review sessions built throughout, skills are deeply reinforced through doing, not just watching. Every graduate walks away with mathematical maturity, a strong calculus foundation for university-level study, and the problem-solving mindset that STEM careers demand.

Learning Objectives

By the end of this course, students will be able to:

• Strengthen and master algebra foundations — equations, inequalities, polynomials, factoring, and rational expressions

• Understand and work fluently with functions — their notation, graphs, transformations, composition, and inverses

• Apply exponential, logarithmic, and trigonometric functions with confidence across equations and graphs

• Develop deep conceptual understanding of limits — graphically, numerically, and algebraically

• Apply limit laws and the formal definition of continuity, including the Intermediate Value Theorem

• Understand the derivative as both a rate of change and the slope of a tangent line

• Apply the full set of differentiation rules: Power, Product, Quotient, and Chain Rules

• Differentiate trigonometric, exponential, and logarithmic functions fluently

• Use derivatives to analyze function behavior — critical points, increasing/decreasing intervals, concavity, and inflection points

• Solve real-world optimization problems and related rates using calculus

• Sketch accurate curves of functions using first and second derivative analysis