Calculus

Course Overview:

This Calculus online course is designed with the intent for students to incorporate the concepts of all previous math courses and expand upon these concepts with the implementation of limits. Emphasis is placed upon the multi-representational approach to calculus where problems and their solutions are explored and interpreted graphically, numerically, analytically, and verbally. Students will also be required to explain their answers in written form and will be asked to compare their written response to the grading rubric and explain why they feel they should receive that grade. Students are required to use graphing calculators. These calculators will be used in a variety of ways including multi-representation of equations (graphs and tables) and for conducting explorations with various functions and how different values change the look of the function.

Semester 1:  

In the first semester of this course, students will explore a wide range of mathematical concepts. They will start by learning about functions, including identifying independent and dependent variables, finding domains and ranges, and graphing linear and exponential functions. The course will cover logarithmic functions, trigonometric functions, and the properties of polynomials and rational functions. Students will also study limits, continuity, and differentiability, and learn to calculate derivatives using various techniques such as the power rule, product rule, quotient rule, chain rule, and implicit differentiation. They will investigate applications such as optimization, related rates, and the use of L’Hopital’s Rule in evaluating limits. Additionally, students will work with parametric equations and study real-world problems related to rates of change, marginal analysis, and geometric optimization.

Semester 2: 

In the second semester, students will dive deeper into calculus concepts, focusing on integration and its applications. They will learn to evaluate definite integrals, understand the Fundamental Theorem of Calculus, and apply integration techniques such as substitution, integration by parts, and the use of algebraic identities and trigonometric substitutions. Students will explore differential equations, including how to solve them and understand their solutions. The course will cover concepts such as the equations of motion, approximate integration using Riemann sums, and improper integrals. Additionally, students will study areas and volumes, applying integration to geometry, and solve differential equations using methods like separation of variables and slope fields. Through these topics, students will gain a deeper understanding of mathematical modeling and problem-solving techniques in various real-world contexts.