Unit 1: Differentiation (Exam: February 21) Slope and derivative, 2.1–2.3 Velocity and rates of change, 2.4 Limits and continuity, 2.5, Notes C Product and quotient rules, 3.1–3.2 Chain rule, 3.3 Exp and log functions, 8.1–8.4 (skip integration) Trigonometric functions, 9.1–9.2, 3.4 Implicit differentation, 3.5 Higher derivatives, 3.6 Unit 2: Applications of differentiation (Exam: March 14) Mean Value Theorem, 2.6 (through MVT) Approximations, Notes A Curve sketching, 4.1–4.2 Max-min problems, 4.3–4.4 Related rates, 4.5 Newton’s method, 4.6 L’Hôpital’s Rule, 12.1–12.3 Unit 3: Integration (Exam: April 4) Differentials, 5.1–5.2 Indefinite integrals, 5.3 Definite integrals, 6.1–6.4 Fundamental Theorem of Calculus, 6.5–6.6, Notes FT Properties of definite integrals, 6.7, Notes PI Numerical integration, 10.9 Unit 4: Applications of integration (Exam: April 25) Differential equations: Separation of variables, 5.4, 8.5 Areas between curves, 7.1–7.2, Notes AV Volumes of solids of revolution, 7.3–7.4 Arclength, 7.5 Surface area, 7.6 Polar coordinates: Area and arclength, 16.4–16.5 Unit 5: Techniques of integration (Exam: May 9) Inverse trig and hyperbolic functions, 9.5, 9.7 Integration by substitution, 10.1–10.3 Integration by inverse substitution, 10.4–10.5 Partial fractions, 10.6, Notes F Integration by parts, 10.7–10.8 Improper integrals, 12.4, Notes INT