A Rapid Introduction To Calculus

This very short calculus course, "A Rapid Introduction to Calculus, is meant for the student looking for a brief and solid introduction to the concepts and techniques of calculus and not really wishing to delve deeply into this subject. Here is a breakdown of the curriculum of this course:

1. Mathematical Preliminaries:

- Review of elementary algebraic concepts and techniques.

- Introduction to mathematical notation and terminology.


2. Functions:

- Definition and properties of functions.

- Types of functions: Linear, quadratic, exponential, trigonometric, and others.

- Notation for functions and basic operations with functions.

3. Limits:

- Introduction to the concept of a limit.

- Finding limits of functions algebraically and graphically.

This also involves the intuitive definition of a limit.

Cannot Be Determined

4. Continuity
Definition of continuity. Detective work: to find points of discontinuity. Intermediate Value Theorem.

5. Differentiability
Introduction to the derivative of a function. Rules for differentiating mathematical expressions.

- Concept of instantaneous rate of change.

6. Key Theorems about the Derivative:

- Rolle's Theorem and the Mean Value Theorem.

- Applications of the Mean Value Theorem.

- The relationship between the derivative and what functions look like.

7. Graphing Functions:

- What functions look like in terms of their first and second derivatives.

- Graphs of functions.

Local extrema and inflection points.

Local extrema Inflection points

8. Integration:

Introduction to the concept of integration.

Calculation of definite and indefinite integrals.

Basic techniques of integration, including substitution and integration by parts.

This course is designed so that it will equip a student with a good foundation in calculus, covering the necessary essential topics so that one may understand how to work with calculus concepts. It is more suitable for people who need quickly to get hold of the basics of calculus for their academic needs or for professional purposes and concentrate on main concepts and practical applications.