Mount Holyoke College
Math 101 (01): Calculus I & Analytic Geometry
Introduction to derivative
- Power, constant, sum rules (Chapter 1). Slope and tangent line
- Product, quotient rules ( Chapter 3).
- Chain rule (Chapter 4).
- Implicit diffentiation (Chapter 4).
- Extended power rule (Chapter 5).
Differentiation of elementary functions
- Trigonometric review: triangles, trigonometric formulas
(Chapter 6, two classes).
- Trigonometric review: periodic functions. Derivative of sin
and cos (Chapter 6).
- exp and log basic properties.
e as a limit. (Chapter 9).
- Derivatives of ex and ln x (Chapter 9).
- Exponential growth. Exponential decay. Rates of growth
(Capter 10 and Chapter 7).
- Max/Min problems (Chapter 7).
- Real-world problems (Chapter 8, two classes).
- Second derivative. Concavity. Acceleration (Chapter 11).
- Curve sketching (Chapter 11, two classes).
Introduction to integral
- Antiderivatives. Differential equations (Chapter 12).
- Area. Definite integral (Chapter 15).