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 |