11th Grade Constructing Linear & Exponential Functions Interactive Videos

Explore exponential and logarithmic functions with a focus on understanding transformations and their impact on graphs and asymptotes. Develop the skills to identify and apply various transformations, refine graphing techniques, and construct new functions effectively.

Investigate the innovative architectural methods employed in constructing the dome of St Paul's Cathedral, with a focus on overcoming engineering challenges and applying mathematical models. Gain insights into structural engineering principles to enhance understanding of historic architectural collaborations and the role of mathematics in design.

Explore the key concepts of eigenvalues and eigenvectors to solve linear homogeneous systems of ordinary differential equations. Develop the ability to apply the eigenvalue method to determine the general solution, enhancing skills in calculating eigenvectors and comprehending their role in the exponential functions of matrices.

Explore the fundamental principles of algebra by examining definitions, properties, and assessments related to linear functions. Achieve a comprehensive understanding of how to identify and evaluate functions, enhancing analytical skills and mathematical reasoning that are essential for algebraic proficiency.

Investigate the characteristics of exponential growth and decay through graphical representation and mathematical analysis. Develop the ability to compare exponential functions and understand their behavior, enhancing skills in graphing and algebraic manipulation.

Explore the intricacies of the Dirac delta function, focusing on its properties and role in modeling sudden system changes. Understand its applications in physics and differential equations through comprehensive analysis. Learners will develop the skills to define and graph the Dirac delta function, interpret its role in differential equations, and apply these insights to comprehend complex physical systems.

Develop proficiency in applying the chain rule to differentiate exponential functions by focusing on essential concepts such as nested functions and substitution techniques. Enhance your skills in finding derivatives of composite functions to improve problem-solving abilities in calculus.

Investigate how Euler's formula connects exponential functions to trigonometric relationships, influencing complex number theory and engineering applications. Gain understanding of the fusion of mathematics with real-world phenomena, enhancing skills in solving differential equations and analyzing circuit systems using sinusoidal principles.

Learn how to differentiate exponential functions by converting them to base e, exploring their relationship with logarithms to simplify calculations. Gain proficiency in applying the chain rule to streamline differentiation processes and gain insights into the role of scale factors in modeling exponential growth. Develop analytical skills essential for assessing mathematical functions and equations.

Explore logarithms with a focus on their role as inverses of exponential functions. Understand the properties of logarithmic functions and gain practical experience in calculating logarithms using various bases. This facilitates a deeper mathematical comprehension and solidifies foundational skills in dealing with exponential relationships.

Explore the application of exponential functions in investment models, focusing on continuous compounding and properties of exponents. Understand how to simplify expressions and transform exponential models to effectively analyze unfamiliar scenarios.

Explore Euler's formula in the context of AC circuit analysis, understanding its ability to connect exponentials with trigonometric functions. Grasp how this relationship simplifies complex circuit problems and facilitates efficient solutions. Learners will develop a deeper comprehension of mathematical transformations in electrical engineering, enhancing their analytical skills in circuit analysis.

Understand the core principles of exponential functions and their roles in various real-world applications, such as compound interest and growth models. Gain a comprehensive grasp of the mathematics that describe these phenomena and develop the competency to identify and analyze the essential components of exponential models.

Exponential functions and logarithms are explored, focusing on their properties, derivatives, and real-world applications, including modeling growth and decay. Learners will gain a deeper understanding of inverse relationships and enhance their ability to apply calculus concepts to solve complex mathematical problems.