This module introduces approximations and infinitesimals, teaching students how to use these concepts in calculus to simplify complex problems.
Key topics include:
This module introduces the concept of derivatives, focusing on their interpretation as slope, velocity, and rate of change. Students will learn how to calculate derivatives using various rules and methods.
Key topics include:
This module covers the essential concepts of limits and continuity, with a focus on trigonometric limits. Students will learn how these concepts form the foundation for calculus.
Topics include:
This module focuses on the derivatives of products and quotients, as well as the derivatives of sine and cosine functions. Students will learn how to differentiate complex functions effectively.
Key areas of study include:
This module introduces the chain rule and higher derivatives, emphasizing their application in differentiating composite functions. Students will explore how to calculate higher order derivatives.
Topics include:
This module covers implicit differentiation and inverse functions. Students will learn techniques for differentiating equations that are not easily solvable for one variable.
Key learning points include:
This module continues the study of hyperbolic functions and prepares students for Exam 1. Topics will cover the properties of hyperbolic functions and their derivatives.
Students will focus on:
This module introduces linear and quadratic approximations, teaching students how to use derivatives to estimate function values near a point.
Key concepts include:
This module focuses on curve sketching, teaching students how to analyze functions using derivatives to understand their behavior and shape.
Topics include:
This module covers max-min problems, guiding students through optimization techniques using derivatives to solve real-world scenarios.
Key components include:
This module introduces related rates, emphasizing how to relate the rates of change of different variables in real-world contexts.
Key topics include:
This module serves as a preface to sets, functions, and limits, introducing students to foundational concepts necessary for understanding calculus.
Key learning points include:
This module delves into analytic geometry, focusing on the intersection of algebra and geometry, and how these concepts can be applied in calculus.
Topics include:
This module covers inverse functions, teaching students how to find and understand the relationship between functions and their inverses.
Key concepts include:
This module revisits sets, functions, and limits, focusing on their relationship with derivatives and the understanding of limits in calculus.
Key areas of study include:
This module presents a more rigorous approach to limits, introducing students to formal definitions and methods of evaluating limits in calculus.
Topics include:
This module discusses mathematical induction as a fundamental concept, providing students with tools to prove statements in calculus and beyond.
Key learning points include:
This module covers the derivatives of some simple functions, allowing students to practice and master basic differentiation techniques.
Key concepts include:
This module introduces approximations and infinitesimals, teaching students how to use these concepts in calculus to simplify complex problems.
Key topics include:
This module focuses on composite functions and the chain rule, guiding students through the process of differentiating nested functions.
Key concepts include:
This module covers the differentiation of inverse functions, teaching students how to find derivatives of functions that have been inverted.
Key learning points include:
This module focuses on implicit differentiation, providing insights into how to differentiate functions defined implicitly rather than explicitly.
Key topics include:
This module examines the relationship between differentiation and continuity, emphasizing their interconnectedness in understanding calculus concepts.
Key learning points include:
This module focuses on the application of differentiation for curve plotting, teaching students how to represent functions graphically based on their derivatives.
Key topics include:
This module addresses differentiation related to maxima and minima, helping students identify optimal solutions for given functions through calculus.
Key components include:
This module discusses Rolle's Theorem and its consequences, teaching students about this fundamental theorem in calculus and its implications for derivative behavior.
Key learning points include:
This module focuses on inverse differentiation, exploring techniques for finding derivatives of inverse functions in various contexts.
Key concepts include:
This module introduces the concept of the "definite" indefinite integral, discussing the relationship between integration and differentiation in calculus.
Key topics include:
This module delves into circular functions, teaching students about their properties and applications in calculus.
Key learning points include:
This module covers inverse circular functions, helping students understand their properties and how to differentiate them.
Key topics include:
This module focuses on the definite integral, teaching students how to calculate and interpret definite integrals in various contexts.
Key learning points include:
This module discusses the marriage of differential and integral calculus, illustrating the connections between the two branches through real-world applications.
Key areas of study include:
This module introduces three-dimensional area, extending the concepts of area calculation into three dimensions and its applications.
Key concepts include:
This module focuses on one-dimensional area, teaching students how to calculate area under curves using integration techniques.
Key areas of study include:
This module covers logarithms without exponents, exploring the properties and applications of logarithmic functions in various contexts.
Key learning points include:
This module discusses inverse logarithms, helping students understand their properties and applications within mathematical contexts.
Key concepts include:
This module emphasizes the significance of signs in mathematical expressions, teaching students how different signs can affect calculations in calculus.
Key topics include:
This module introduces inverse hyperbolic functions, teaching students their definitions, properties, and differentiation techniques.
Key concepts include:
This module covers advanced integration techniques, focusing on basic recipes for integration, essential for solving complex problems in calculus.
Key areas of study include:
This module explores more integration techniques, focusing on partial functions and how to integrate them effectively in calculus.
Key topics include:
This module covers integration by parts, teaching students this powerful technique for integrating products of functions in calculus.
Key concepts include:
This module discusses improper integrals, teaching students how to evaluate integrals that do not have defined limits or finite values.
Key areas of study include:
This module introduces infinite series, focusing on their convergence properties and importance in calculus.
Key learning points include:
This module focuses on positive series, teaching students how to analyze and work with series that converge to positive values.
Key concepts include:
This module discusses absolute convergence, focusing on series that converge regardless of the arrangement of their terms.
Key learning points include:
This module explores polynomial approximations, teaching students how to use series to approximate functions and their values.
Key points include:
This module discusses uniform convergence, emphasizing its importance in the context of infinite series and functions.
Key concepts include: