### Requirements

- Basic math skills: You should have a strong foundation in algebra, geometry, and trigonometry. You should also be familiar with functions, equations, and graphs. In order to succeed in this class, you need to review Pre-Calculus. To be more specific, review the following topics.
- Numbers and the real line: intervals, absolute value, equations and inequalities.
- Cartesian coordinates: Axis scales, increments and distances, graphs, straight lines, equations of lines.
- Functions and their graphs: domain convention, graphs of functions, even and odd functions, symmetry and reflection, and piecewise functions.
- Trigonometric functions: sine, cosine, tangent, cotangent, secant, cosecant, and some useful identities, some special angles.
- Combining functions to make new functions: sums, differences, products, quotients, multiples, composite functions
- Polynomials and rational functions: roots and factors, roots and factors of quadratic polynomials.
- Square root and the conjugate.
- Equation of lines, the slope of a line.
- Exponentials, logarithms, and their properties.
- Time commitment: A calculus course can be demanding and requires a significant time commitment outside class to complete assignments, practice problems, and study the material.

### Features

- This course is typically designed for students new to the subject and may require a solid mathematical background. The key features of such a course could include the following:
- Fundamentals of Calculus: This course will cover the fundamental concepts of calculus, such as limits, derivatives, and integrals, and how they relate.
- Emphasis on conceptual understanding: This course in calculus prioritizes developing students' understanding of the concepts and building their intuition for applying them rather than just memorizing formulas.
- Emphasis on problem-solving: This course involves a lot of problem-solving, providing plenty of opportunities for students to practice and apply their skills to various problems.

### Target audiences

- This introductory course to calculus could be suitable for the following:
- Students in high school who are starting their first calculus course as part of their advanced math curriculum
- Students in college who must take a calculus course to pursue a degree in a STEM (science, technology, engineering, or mathematics) field
- Adult learners who are interested in learning calculus on their own, either for personal interest or to prepare for advanced studies or a career change.
- Educators who are seeking a comprehensive overview of calculus to improve their teaching methods or to develop new teaching materials.
- Anyone who has a basic understanding of algebra, geometry, and trigonometry, and wants to learn more about the fundamental concepts of calculus.

Calculus is a branch of mathematics that deals with the study of rates of change and how things change over time. It is a powerful tool for analyzing and solving problems in fields such as physics, engineering, economics, and more.

Some of the key topics in calculus include:

- Limits: Limits are used to describe the behaviour of a function as the input approaches a certain value, such as infinity or zero.
- Derivatives: Derivatives are used to describe the instantaneous rate of change of a function at a particular point. They are also used to find the slope of a tangent line to a curve at a specific point.
- Applications of Derivatives: The applications of derivatives include optimization problems, finding critical points, and graphing functions.
- Integrals: Integrals are used to find the area under a curve, as well as to calculate the total change in a function over a given interval.
- Applications of Integrals: Applications of integrals include calculating volumes, calculating work done by a force, and calculating probabilities.
- Sequences and Series: Sequences and series involve the study of infinite sets of numbers, including their convergence and divergence.

Here is a detailed list of topics that will be covered in this introductory calculus course:

- Functions and graphs
- Domain and range
- Graphing techniques
- Composite functions
- Inverse functions
- Exponential and logarithmic functions

- Limits and continuity
- Definition of limit
- Limits at infinity
- One-sided limits
- Continuity of a function

- Derivatives and differentiation
- Definition of derivative
- Derivatives of polynomials, exponential, logarithmic, and trigonometric functions
- Product, quotient, and chain rules of differentiation
- Implicit differentiation
- Related rates

- Applications of derivatives
- Critical points and extrema
- First and second derivative tests
- Optimization problems
- Graphing and analysis of functions
- Newton’s method
- L’Hôpital’s rule

- Integration and antiderivatives
- Definition of antiderivative
- Indefinite and definite integrals
- Integration by substitution
- Integration by parts
- Partial fractions
- Trigonometric substitution

- Applications of integration
- Area and volume
- The average value of a function
- Arc length
- Surface area
- Work and fluid force

Calculus is a foundational subject in higher mathematics and is a prerequisite for many advanced courses in science and engineering. The target audience for calculus generally includes students who have completed high school mathematics and are pursuing studies in science, engineering, economics, or other fields that require a strong mathematical background. Many university programs require students to pass a Calculus course.

## Leave a Reply