**Instructors:** Lizzie Buchanan, Nadia LafreniÃ¨re, Misha Tyomkin.

**Course on Canvas:** https://canvas.dartmouth.edu/courses/50321/ ⇗

## Syllabus

Day Date Section Topic 1 1/5 V2, 6.3 ("Taylor polynomials") Taylor polynomials 2 1/7 V2, 5.1 Limits of Taylor polynomials 3 1/10 V2, 5.2, 5.4, 5.5, 6.3 ("Overview of Taylor/Maclaurin Series") Limits of Taylor series 4 1/12 V2, 6.3 ("Taylorâ€™s Theorem with Remainder") Approximations and error bounds 5 1/14 V2, 5.6 ("Ratio test"), 6.1, 6.2, 6.3 ("Representing Functions with Taylor and Maclaurin Series") Taylor series as functions (power series) 6 1/17 Canceled (MLK day) 7 1/19 V2, 1.1, 1.2, 2.2 Riemann sums 8 1/21 V2, 2.2, 2.3 Volumes of Revolution 9 1/24 V2, 2.5 Applications of integration End of content for first midterm 10 1/26 V3, 2.2 3-D coordinate systems, distance, equations of spheres 1/27 Midterm 11 1/28 V3, 2.1 Vectors, displacement, velocity 12 1/31 V3, 2.3 Dot product, projections, work in 3-D 13 2/2 V3, 2.4 Cross product 14 2/4 V3, 2.5 Lines and planes 15 2/7 V3, 2.6, 3.1 Curves and surfaces, parametrized curves, motion in space 16 2/9 V3, 3.2 Derivatives and integrals of vector-valued functions 17 2/11 V3, 3.3 Arc length 18 2/14 V3, 3.4 Motion along a curve End of content for second midterm 19 2/16 V3, 4.1 Graphs and level sets 2/17 Midterm 20 2/18 V3, 4.2 Functions of several variables: limits and continuity 21 2/21 V3, 4.3 Partial derivatives 22 2/23 V3, 4.4 Tangent planes 23 2/25 V3, 4.4 Derivative as linear approximation 24 2/28 V3, 4.5 Chain Rule 25 3/2 V3, 4.6 Directional derivatives and gradient vector 26 3/4 V3, 4.7 Maximum and minimum values 27 3/7 V3, 4.8 Constrained optimization