| Chapter | Topics | Lecture hours |
| P |
Preview and review: functions, absolute values, inequalities,
preview of calculus | 3 |
| 1 |
Limits and rates of change: limits of sequences and functions,
limit laws, continuity, Intermediate Value Theorem
| 5 |
| 2 |
Derivatives: tangents and differentiability,
higher derivatives, differentiation formulae (including chain rule),
implicit differentiation, Mean Value Theorem and applications
(monotonicity, concavity)
| 10 |
| 3 |
Elementary functions: inverse functions and their derivatives,
derivatives of trig and inverse trig functions, exponential and
logarithmic functions and their derivatives, exponential growth and
decay
| 7 |
| 4 |
Applications: curve sketching, maximum and minimum problems,
related rate problems, l'Hopital's rule
| 8 |
| 4 |
Approximation: linearization (with error estimate), quadratic and
higher approximations, Taylor polynomials and Taylor's theorem with Lagrange
remainder, Taylor series for exp, sin, cos
| 7 |