Math 251

Engineering Mathematics III
Joe Kahlig

Lecture Notes


The class notes contain the concepts and problems to be covered during lecture. Printing and bringing a copy of the notes to class will allow you to spend less time trying to write down all of the information and more time understanding the material/problems. Additional examples may be included during the lectures to clarify/illustrate concepts.

As an alternate to taking notes on paper, consider taking notes on your laptop using OneNote, or a similar program.

Completed notes will be posted after the section has been finished. Be advised that the notes may not included everything that is said during class.
The problems will be completely worked out but some additional information (hints, warnings, analysis of the problem,..) may not we written out in the notes.

Exam 1 Material
Section Notes Solutions videos Additional
Problems
Additional Problem Solutions
12.1: Three Dimensional Coordinate Systems blank completed video
video pdf
questions solutions
12.2: Vectors blank completed video
video pdf
questions solutions
12.3: The Dot Product blank completed video
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questions solutions
12.4: The Cross Product blank completed part a
part b
video pdf
questions solutions
12.5: Equations of Lines and Planes blank completed part a
part b
part c
video pdf
questions solutions
12.6: Quadratic Surfaces
Quadratic chart
blank watch video for concepts video
video pdf
13.1: Vector Functions and Space Curves blank completed part a
part b
video pdf
questions solutions
13.2: Derivative and Integrals of Vector Functions blank completed video
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questions solutions
13.3: Arc Length and Curvature blank completed part a
part b
video pdf
questions solutions
13.4: Motion in Space: Velocity and Acceleration blank video
video pdf
Exam 1 Info. info



Exam 2 Material
Section Notes Solutions videos Additional
Problems
Additional Problem Solutions
14.1: Functions of Several Variables blank completed part a
part b
video pdf
questions solutions
14.3: Partial Derivatives blank completed part a
part b
video pdf
questions solutions
14.4: Tangent Planes and Differentials blank completed part a
part b
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questions solutions
14.5: The Chain Rule blank completed part a
part b
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questions solutions
14.6: Directional Derivatives and the Gradient Vector blank completed part a
part b
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questions solutions
14.7: Maximum and Minimum Values blank completed part a
part b
part c
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questions solutions
14.8: Lagrange Multipliers blank completed part a
part b
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questions solutions
Exam 2 Info. info



Exam 3 Material
Section Notes Solutions videos Additional
Problems
Additional Problem Solutions
10.3: Review of Polar Coordinates
You should review this section on your own. This material was covered in Math 152.
blank part a
part b
part c
video pdf
15.1: Double Integrals over Rectangles blank completed part a
part b
video pdf
questions solutions
15.2: Double Integrals over General Regions
Math 152 lecture notes on Integration: see 7.1, 7.2, 7.3, 7.4
blank completed part a
part b
part c
video pdf
questions solutions
15.3: Double Integrals in Polar Coordinates blank completed part a
part b
video pdf
questions solutions
15.4: Applications of Double Integrals blank
completed video
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questions solutions
15.5: Surface Area blank completed video
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questions solutions
15.6: Triple Integrals blank completed part a
part b
part c
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questions solutions
15.7: Triple Integrals in Cylindrical Coordinates blank completed video
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questions solutions
15.8: Triple Integrals in Spherical Coordinates blank completed part a
part b
part c
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questions solutions
15.9: Change of Variables blank completed part a
part b
part c
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questions solutions
Exam 3 Info. info

Final Exam Material
Section Notes Solutions videos Additional
Problems
Additional Problem Solutions
The material from 14.7 (the section over absolute maximum and absolute minimum) will also be on the final exam.
16.1: Vector Fields blank completed video
video pdf
16.2: Line Integrals blank completed part a
part b
part c
video pdf
questions solutions
16.3: Fundamental Theorem for Line Integrals blank completed part a
part b
video pdf
questions solutions
16.4: Green's Theorem blank completed part a
part b
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questions solutions
16.5: Curl and Divergence blank completed video
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questions solutions
16.6: Parametric Surfaces and Their Areas blank partial part a
part b
video pdf
questions solutions
16.7: Surface Integrals blank part a
part b
part c
video pdf
questions solutions
16.8: Stokes' Theorem blank part a
part b
video pdf
questions solutions
16.9: Divergence Theorem blank video
video pdf
questions solutions
Final Exam Info. info Disclaimer: The following should not be used as your sole source of preparation for the exam. You should also review lecture notes, Week-in-Review notes, and homework. I have not looked at this sample exam nor have I looked at the solutions.
sample Final from Amy Austin
sample Final solutions from Amy Austin