Calculus, Part 1

This is the course web page for the course Calculus, Part 1.

What you will get from this course: Completing this course will provide you with a solid understanding of the fundamental concepts of calculus and skill in performing basic operations of calculus. You will also have the opportunity to practice these skills throughout the course, and to get feedback on your practice so that you will know what you have to work on to improve. You will learn how to apply what you have learned to solve important practical problems. This course will help you to prepare for the fast pace of university courses.

Abstract concepts are presented step by step, in simple concrete settings first, and then gradually building up to more general and more abstract settings. This will help you to gain in mathematical maturity and you will be better able to cope with abstract material at university. You will be continually challenged to relate the symbolic, algebraic calculations with their geometric and physical interpretations, which will lead you to a much deeper understanding of the material, and will help you to become a better practitioner of calculus tools. All of this will accelerate your progress once you reach university.

Textbook material for this course is found here.


  • Basic ideas of calculus
  • Slope of line; rate of change of a quantity
  • The idea of a limit
  • Practical limit calculations
  • The formal definition of a limit; advanced calculations
  • The derivative
  • Determining derivatives for various kinds of functions
  • Applications of derivatives
  • Basic ideas of integration
  • The fundamental theorem of calculus
  • Some techniques of integration
  • Applications of integration
  • Simple differential equations
  • An introduction to infinite series of numbers
  • An introduction to power series

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