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Calculus is one of humanity's greatest achievements, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the fundamental concepts of single-variable calculus, with a focus on conceptual understanding and applications. The course is ideal for students who are just starting out in engineering, physical science, and social science. The course distinguishes itself through the following features:
- The introduction and use of Taylor series and approximations from the start;
- a novel synthesis of discrete and continuous forms of Calculus;
- an emphasis on the conceptual over the computational; and
- a clear, dynamic, unified approach.
Syllabus :
1. A Review of Functions
- Functions
- Exponentials
2. Taylor Series
- Taylor Series
- Computing Taylor Series
- Convergence
- Expansion Points
3. Limits and Asymptotics
- Limits
- l'Hôpital's Rule
- Orders of Growth
