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Columbus State Community College

Calculus & Analytical Geometry IV/Multivariable Calculus, Math 254

 

Course Description (from the College):  MATH 254 presents an introduction to multivariable calculus. Topics includes vector valued functions and motion in the plane and in space, functions of several variables, partial derivatives, directional derivatives, gradients, extrema, multiple integrals, line integrals and Green’s Theorem. Course topics have applications to problems in science and engineering. Meets general education requirement for the A.S. and A.A. degrees.   Prerequisite: Math 153 with a grade of C or better.

*Files on this page are mostly in .docx format. If you have difficulty downloading them, see instructions linked in the left margin.

Syllabus -- in Word format

Homework

Important Dates
Exam I  -- Tuesday, January 24th exam key/study guide key
Exam II  -- Tuesday, February 14th exam key: even odd/study guide key
Exam III  -- Tuesday, March 6th exam key: even odd/study guide key
Final Exam -- Tuesday, March 13th at 6:00 p.m. exam key

more detailed schedule in the syllabus

Email List

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Grade Calculator -- javascript online grade calculator

Announcements:

Math Adjunct Office # DH 431
My CSCC email: bmccall2@cscc.edu
Calc & Stat Lab: M-Th 8-5 (roughly), MWTh Room is TBA (check the schedule outside the algebra lab DH 313).  Additional hours may be available at other campuses, or in the algebra lab before or after calc lab hours (check for tutors who also work the calc lab).  Not all calc tutors can do this level of calculus.

 

Answer Keys

Quiz #1 -- key
Quiz #2 -- key
Quiz #3 -- key
Quiz #4 -- key
Quiz #5 -- key
Quiz #6 -- key
Quiz #7 -- key
Quiz #8 -- key
Quiz #9 -- key
Quiz #10 -- key
Quiz #11 -- key
Quiz #12 -- key
Quiz #13 -- key
Quiz #14 -- key
Quiz #15 -- key
Quiz #16 -- key

Homeworks to be Turned in

Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Homework #6

 

Suggested Homework

Section

Suggested Problems (eoo=every other odd)

12.1

1-20 odd, 23-38 eoo, 59-66 odd, 69-79 odd

12.2

1-6 odd, 9-26 eoo, 39, 49-61 odd, 63-68 eoo

12.3

1-22 eoo, 25-48 odd

12.4

5-16 odd, 21-56 eoo

12.5

1-14 odd, 21-46 eoo

13.1

1-28 eoo, 31-28 odd, 45-48, 49-60 eoo

13.2

1-62 eoo, 71-75 odd

13.3

1-40 eoo, 45-48 odd, 51-68 odd, 73-86 odd

13.4

1-20 eoo

13.5

1-42 eoo

13.6

1-50 eoo, 55-62 odd

13.7

1-34 eoo, 41-46 odd, 49-54 odd

13.8

1-34 eoo, 45-62 eoo

13.9

1-21 odd

13.10

5-22 odd, 27

14.1

1-74 eoo

14.2

7-42 odd, 49-56 odd

14.3

1-32 eoo, 37-42 odd

14.4

1-26 eoo

14.5

1-18 odd, 29-34 odd

14.6

1-42 eoo

14.7

1-26 odd

14.8

1-22 odd, 27

15.1

1-16 odd, 21-46 odd, 51, 55-64 odd, 69-76 odd

15.2

1-39 eoo, 53-60 odd

15.3

1-34 odd

15.4

1-4 odd, 7-20 odd, 25-28 odd

15.5

1-42 eoo

*eoo = every-other odd, for practice problems, it doesn’t matter to me whether you do 1,5, 9, 13, etc., or if you do 3, 7, 11, 15, etc.

Chapter 12 Application Problems -- key
Chapter 13 Application Problems -- key
Chapter 14 Application Problems -- key
Chapter 15 Application Problems -- key

Handouts

Common 3D Surfaces
Tangents & Normals
Line Integrals
Lagrange Mulitpliers
Relative & Absolute Extrema
Implicit Differentiation
Triple Integrals
Vector Fields
Del-Notation
Limits in 2 or more Variables
Graphing in 3D

 

Proofs

12.2 Properties of the Derivative
12.9 Curvature
13.0 Partial Derivatives & Notation
13.4 Sufficient Conditions for Differentiability
13.5 Differentiability Implies Continuity
13.6 Chain Rule: One Independent Variable
13.9 Directional Derivative
13.11 The Gradient
13.19 Lagrange's Theorem
14.5 Change of Variables for Double Integrals
15.1 Test for Conservative Vector Fields
15.5 Fundamental Theorem of Line Integrals
15.6 Independence of Path for Conservative Vector Fields
15.8 Green's Theorem

 

Links:

Programs for Numerical Methods - TI-83 (pdf)
PDF Graph Paper
I Will Derive song
How to draw Greek
Graphing 3D Parametric Curves
GraphCalc
Plotting Vector Fields
Dimensions
Spring Quarter 2011
Summer Quarter 2011

 

 
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Last updated: 2012 March 13