Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.
This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course encourages you to participate by providing you with:
- instant feedback on practice problems
- interactive graphs and games for you to play
- calculus projects and demos you can try at home
- opportunities for you to explain your thought process
Syllabus
Week One: Functions and Limits
Week Two: Infinity and Continuity
Week Three: Basics of Derivatives
Week Four: Curve Sketching, The Product Rule and Quotient Rule
Week Five: The Chain Rule
Week Six: The Derivatives of Trigonometric Functions and their Inverses
Week Six: The Derivatives of Trigonometric Functions and their Inverses
Week Seven: Applications of Differentiation
Week Eight: Optimization
Week Nine: Linear Approximation
Week Ten: Antiderivatives
Week Eleven: Integrals
Week Twelve: The Fundamental Theorem of Calculus
Week Thirteen: Techniques of Integration
Week Fourteen: Applications of Integration
Week Fourteen: Applications of Integration