MASTER SYLLABUS

2020-2021

A.	Academic Division: Liberal Arts

B.	Discipline: Mathematics

C.	Course Number and Title: MATH2010 Calculus III

D.	Course Coordinator: Sara Rollo

Assistant Dean: Dr. Steve Haynes

Instructor Information:

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E.	Credit Hours: 4

F.	Prerequisites: MATH1151 (Minimum grade of C- required)

G.	Syllabus Effective Date: Fall, 2020

H.	Textbook(s) Title:

On Campus Classes:

Calculus (packaged w/Web Assign)

Author: Ron Larson/Bruce Edwards

Copyright Year: 2018

Edition: 11TH

ISBN # 9781337604741

Off Campus Classes (at High Schools):

Calculus (packaged w/Web Assign)

Author: Ron Larson/Bruce Edwards

Copyright Year: 2014

Edition: 10TH

ISBN # 9781305718661

I.	Workbook(s) and/or Lab Manual:	Supplies: TI-83 or TI-84 required

J.	Course Description: This is the third of three courses in the basic calculus sequence. Topics include vector functions, functions of two or more variables, gradients, tangent planes and normal lines, Lagrange multipliers, partial derivatives (including applications), arc length and curvature, multiple integration, implicit and parametric calculus, spherical and cylindrical coordinates, Jacobians to change variables, and vector calculus including Green’s Theorem and Stoke’s Theorem. This course meets the requirements for OTM Calculus III TMM018 and also TAG# OMT018.

K.	College Wide Learning Outcomes:

College-Wide Learning Outcomes	Assessments - - How it is met & When it is met
Communication – Written
Communication – Speech
Intercultural Knowledge and Competence
Critical Thinking
Information Literacy
Quantitative Literacy

L.	Course Outcomes and Assessment Methods:

Upon successful completion of this course, the student shall:

Outcomes	Assessments – How it is met & When it is met
Differentiate and integrate vector-valued functions. For a position vector function of time, interpret these as velocity and acceleration.	HW, Test, Final exam Weeks 1,2,4 and 16
Evaluate limits, determine the continuity, determine the differentiability and describe the graphs of functions of several variables.	HW, Test, Final exam Weeks 2,3, 4 and 16
Find arc length and curvature of space curves.	HW, Test, Final exam Weeks 2,4 and 16
Find partial derivatives, directional derivatives, gradients, and differentials of functions of several variables and use them to solve applied problems.	HW, Test, Final exam Weeks 5,6,7,8 and 16
Find equations of tangent planes and normal lines to surfaces that are given implicitly or parametrically.	HW, Test, Final exam Weeks 4,5,8 and 16
Apply differentials of functions of several variables to optimization problems.	HW, Test, Final exam Weeks 6,7,8, 12 and 16
Use Lagrange multipliers to solve constrained optimization problems.	HW, Test, Final exam Weeks 8,12 and 16
Evaluate multiple integrals in appropriate coordinate systems such as rectangular, polar, cylindrical and spherical coordinates.	HW, Test, Final exam Weeks 10,12 and 16
Use Jacobians to change variables in multiple integrals.	HW, Test, Final exam Weeks 11, 12 and 16
Use the Fundamental Theorem of Line Integrals to solve applied problems.	HW, Test, Final exam Weeks 9,10, 12 and 16
Identify conservative and inverse square fields.	HW, Test, Final exam Weeks 12 and 16
Find the curl and divergence of a vector field, the work done on an object moving in a vector field, and the flux of a field through a surface.	HW, Test, Final exam Weeks 13,14 and 16
Use Green’s Theorem, the Divergence (Gauss’s) Theorem and Stoke’s Theorem.	HW, Test, Final exam Weeks 15 and 16

M.	Topical Timeline (Subject to Change):

Weeks 1-2	Graph and find the equation of a line and plane in space Graph and find the equations of surfaces in space such as cylinders and quadric surfaces Convert between rectangular, cylindrical and spherical coordinates
Weeks 2-4	Differentiate and integrate vector-valued functions Find the unit tangent vector and principal unit normal vector of a smooth curve and use to find the arc length and curvature Find the tangential and normal components of acceleration for a smooth curve
Weeks 5-8	Describe graphs, level curves and level surfaces of functions of several variables and evaluate limits of functions of several variables Discuss the continuity and differentiability of a function of several variables Find partial derivatives, directional derivatives, gradients and differentials of functions of several variables and use them to solve applied problems Find equations of tangent planes and normal lines to surfaces (including parametric surfaces) Use the chain rule for functions of several variables (including implicit differentiation) Find extrema of functions of several variables using the second partials test and Lagrange multipliers and solve applied problems
Weeks 9-12	Evaluate iterated integrals and use them to find the area of plane regions Evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates and use them to solve applications involving volume, surface area, density, moment and centroids Use a Jacobian to change variables in multiple integrals
Weeks 12-16	Identify conservative and inverse square fields Find the curl and divergence of a vector field and the flux of a field through a surface and solve applied problems Evaluate line and surface integrals (including parametric surfaces) and solve applied problems Identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals Use Green’s Theorem, the Divergence (Gauss’s) Theorem and Stokes’s Theorem

N.	Course Assignments:

Chapter 11 [M. 1-3]

Test 1

Chapter 12 [M. 4-6]

Test 2

Chapter 13 [M. 7-12]

Test 3

Chapter 14 [M. 13-15]

Test 4

Chapter 15 [M. 16-20]

Comprehensive Final Exam

O.	Recommended Grading Scale:

NUMERIC	GRADE	POINTS	DEFINITION
93–100	A	4.00	Superior
90–92	A-	3.67	Superior
87–89	B+	3.33	Above Average
83–86	B	3.00	Above Average
80–82	B-	2.67	Above Average
77–79	C+	2.33	Average
73–76	C	2.00	Average
70-72	C-	1.67	Below Average
67–69	D+	1.33	Below Average
63-66	D	1.00	Below Average
60-62	D-	0.67	Poor
00-59	F	0.00	Failure

P.	Grading and Testing Guidelines:

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Q.	Examination Policy:

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R.	Class Attendance and Homework Make-Up Policy:

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S.	Classroom Expectations:

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T.	College Procedures/Policies:

Important information regarding College Procedures and Policies can be found on the syllabus supplement located at

http://catalog.ncstatecollege.edu/mime/download.pdf?catoid=5&ftype=2&foid=3