MA 242.601 - Spring 2020

Day-by-day Schedule

Week of	Section	Topic
1/06– 1/10	1.1	Chapter 0: Chapter 1.1: Cartesian Coordinates: In 2 and 3 dimensional space
	1.2	Vectors in 2 and 3 Dimensions:
	1.2	Continue study of vectors
	1.3	The Angle Between Two Vectors: The Dot Product
1/13 – 1/17	1.4	The Cross Product:
	1.5	Lines and Planes in 3-dimensional Space
		More on equations of lines and planes
	2.1	The Calculus of Vector-valued Functions: Limits, derivatives and integrals
1/20	Monday	Holiday
1/21 – 1/24	2.2	Parameterized Curves in Space: Newton’s second law. Begin free fall under gravity. Projectile motion under gravity; The isotropic oscillator (Optional)
	2.3	Fundamental Quantities Associated with a Curve: Tangent vectors, arc length and curvature
	2.4	The Intrinsic Geometry of Curves in 3-Space; curvature and the osculating plane
1/27 – 1/31	2.4	More on the geometry of curves in space; the osculating circle, and the normal and tangential components of acceleration
	3.1	Multivariable Functions: Material up through level curves
		Review for Test #1
January 31	Friday	TEST #1 (********** 2-day window: 1/30 or 2/3 *************)
2/3 – 2/7	3.1	Multivariable Functions: Material up through level curves
		Level surfaces of functions of 3 variables. Parametric surfaces.
	3.2	Limits and Continuity: Theorems on limits; Continuity;
	3.3	Directional Derivatives: Partial derivatives; higher derivatives;
2/10 – 2/14	3.3	Geometrical interpretation of partial derivatives; Tangent plane to the graph of f(x,y)
	3.4	Differentiability of multivariable functions: Definition; Differentiability and continuity; Theorem 9 on characterizing differentiability.
	3.5	The Directional Derivative and the Gradient: Formula for the directional derivative in terms of the gradient.
		What does the gradient vector say about a function?
2/17 – 2/21	3.5	The Chain rules for multivariable functions
		Tangent planes to graphs z = f(x,y); The general chain rule
	3.6	Optimization: local and global extreme values of f(x,y)
	3.6	More on extreme values;
		Review for Test #2
Monday, 2/24	Monday	TEST #2 (********** 3-day window: 2/21, 2/24, 2/25 *************)
2/25 - 2/28	4.1	Double Integrals over a rectangle as a limit of Riemann sums
		Fubini’s Theorem for double integrals over rectangles; iterated integrals
	4.1	Double integrals over general regions
3/2 – 3/6	4.1	Reversing the order of integration
	4.2	Applications of Double Integrals
	4.3	Triple Integrals in Cartesian Coordinates: Over rectangular solid regions
3/09 – 3/13		Spring Break
3/16 – 3/20	4.3	Triple integrals over z-simple regions
		Triple integrals over x & y- simple regions; Applications of triple integrals
	5.1	Double Integrals in Polar Coordinates: over polar rectangles
	5.1	Double integrals in polar coordinates over more general regions
3/23 – 3/27	5.2	Triple integrals in cylindrical coordinates
	5.3	Triple integrals in spherical coordinates
	5.3	More on triple integrals in spherical coordinates
		Review for test #3
3/30	Monday	TEST #3 (********** 3-day window: 3/27, 3/30, 3/31 *************)
3/31 – 4/3	6.1	Vector Fields
	6.2	Line Integrals of functions: First briefly review parameterized curves from section 2.2 and formula #2.6 for ds/dt in section 2.3.
	6.3	Line integrals of vector fields: The fundamental theorem for line integrals
	6.3	Conservative vector fields and potential functions; Conservation of total energy
4/6 – 4/10	6.4	Parametric Surfaces in Space: graphs, spheres and cylinders
		Surface Integrals: Surface Area of a Parametric Surface Tangent planes to parametric surfaces
	6.5	Surface Integral of a Function
	6.5	Surface Integral of a Vector Field
4/13 – 4/17	6.5	More on surface integrals of vector fields
4/14		Review for test #4
4/15	Wednesday	TEST #4 (********** 3-day window: 4/14, 4/15, 4/16 *************)
	7.1 7.2	Integral Curves of Vector Fields The Divergence of a Vector Field
4/20 – 4/23	7.2	The Curl of a Vector Field:
	7.3	Green’s Theorems: for circulation and for flux
	7.4, 7.5	Stokes’ Theorem, The Divergence Theorem. LAST DAY OF CLASSES
4/24	Friday	Reading Day
4/27	Monday	Day 1 of 4-day window for FINAL EXAM
4/28	Tuesday	Day 2 of 4-day window for FINAL EXAM
4/29	Wednesday	Day 3 of 4-day window for FINAL EXAM
4/30	Thursday	Day 4 of 4-day window for FINAL EXAM