Calculus: Single Variable Part 1 - Functions

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this first part--part one of five--you will extend your understanding of Taylor series, review limits, learn the why behind l'Hopital's rule, and, most importantly, learn a new language for describing growth and decay of functions: the BIG O

• Understand foundational concepts of single-variable calculus
• Apply Taylor series and approximations in various problems
• Integrate discrete and continuous calculus forms
• Develop a deep conceptual understanding beyond computation

• No deep prior experience required
• Basic computer and internet skills helpful
• Ability to read course instructions in English and complete short practice activities