Week 1: Review of families of functions (incl. algebraic, inverse functions, exponential, logarithmic, trigonometric and inverse trigonometric, piecewise, and parametric curves/functions
Week 2: Tangent and velocity problems, limit of a function, continuity, limits involving infinity
Week 3: Derivatives and rates of change, derivative as a function, derivatives of polynomial and exponential functions, product and quotient rules
Week 4: Derivatives of trig functions, chain rule, derivatives of inverse trig functions, derivatives of log functions
Week 5: Related rates, max and min values, derivatives and shapes of curves, graphing with technology and calculus, indeterminate forms and l'Hospital's rule
Week 6: Optimization problems, Newton's method, antiderivatives, areas and distances
Week 7: The definite integral and their evaluation, fundamental theorem of calculus, integration by substitution
Week 8: Integration by parts, additional techniques of integration
Week 9: Approximate integration (midpoint, trapezoidal and Simpson's rules), improper integrals
Week 10: More about areas, volumes: cross sections and disks
Week 11: Volumes: cylindrical shells, arc length (rectangular functions and parametric curves)
Week 12: Average value of a function, applications to physics and engineering: work, centers of mass, fluid pressure
Week 13: Probability, sequences, series and convergence of series
Week 14: Integral and comparison tests for series, representation of functions as power series, Taylor series