Course Syllabus

This course provides a bridge between algebra and calculus, guiding students through the underlying mathematical concepts needed to understand and appreciate calculus. The course reviews real and complex numbers, functions, and equations and inequalities. It then goes into some detail on specific types of functions, such as polynomials, exponentials, and logarithms. It also provides a derivation of the principles of trigonometry on the basis of simple right-triangle and circle geometry. After reviewing vectors, polar coordinates, and conic sections, the material sets up calculus proper by examining limits as well as sequences and series.

The final lessons of the course use the basic principles of algebra to derive the two key tools of calculus: differentiation (the derivative) and integration (the integral). At the end of this course, students will be prepared to study calculus in greater depth, further investigating and applying derivatives and integrals to solve a variety of math, physics, and other problems.