Week 1-3: Parametric equations and Polar coordinates.
(1) Section 8.1: Arc length
(2) Section 10.1: Curves defined by parametric equations.
(3) Section 10.2: Calculus with plane curves.
(4) Section 10.3 Polar coordinates.
(5) Section 10.4: Areas and lengths in polar coordinates
(6) Section 10.5: Conic sections.
(7) Section 10.6: Conic sections in polar coordinates. (optional)
Weeks 4–6: Vectors and the geometry of space.
(1) Section 12.1: Three-dimensional coordinate systems.
(2) Section 12.2: Vectors.
(3) Section 12.3: The dot product.
(4) Section 12.4: The cross product.
(5) Section 12.5: Equations of lines and planes.
(6) Section 12.6: Cylinders and quadric surfaces.
Weeks 7 - 9: Vector functions.
(1) Section 13.1: Vector functions and space curves
(2) Section 13.2: Derivatives and integrals of vector functions.
(3) Section 13.3: Arc length and curvature.
(4) Section 13.4: Motion in space: velocity and acceleration.
Weeks 10 - 15: Partial derivatives.
(1) Section 14.1: Functions of several variables.
(2) Section 14.2: Limits and continuity
(3) Section 14.3: Partial derivatives.
(4) Section 14.4 Tangent planes and linear approximations
(5) Section 14.5: The chain rule.
(6) Section 14.6: Directional derivatives and the gradient vector.
(7) Section 14.7: Maximum and minimum values.
(8) Discovery project p.1010: Quadratic approximation and critical
points (Taylor’s formula for two variables).
(9) Section 14.8: Lagrange multipliers.
(1) Section 8.1: Arc length
(2) Section 10.1: Curves defined by parametric equations.
(3) Section 10.2: Calculus with plane curves.
(4) Section 10.3 Polar coordinates.
(5) Section 10.4: Areas and lengths in polar coordinates
(6) Section 10.5: Conic sections.
(7) Section 10.6: Conic sections in polar coordinates. (optional)
Weeks 4–6: Vectors and the geometry of space.
(1) Section 12.1: Three-dimensional coordinate systems.
(2) Section 12.2: Vectors.
(3) Section 12.3: The dot product.
(4) Section 12.4: The cross product.
(5) Section 12.5: Equations of lines and planes.
(6) Section 12.6: Cylinders and quadric surfaces.
Weeks 7 - 9: Vector functions.
(1) Section 13.1: Vector functions and space curves
(2) Section 13.2: Derivatives and integrals of vector functions.
(3) Section 13.3: Arc length and curvature.
(4) Section 13.4: Motion in space: velocity and acceleration.
Weeks 10 - 15: Partial derivatives.
(1) Section 14.1: Functions of several variables.
(2) Section 14.2: Limits and continuity
(3) Section 14.3: Partial derivatives.
(4) Section 14.4 Tangent planes and linear approximations
(5) Section 14.5: The chain rule.
(6) Section 14.6: Directional derivatives and the gradient vector.
(7) Section 14.7: Maximum and minimum values.
(8) Discovery project p.1010: Quadratic approximation and critical
points (Taylor’s formula for two variables).
(9) Section 14.8: Lagrange multipliers.