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Lecture Notes
PDF
Section 2, Page 1 to page 3
Maximization and minimization problems are worked through step-by-step. Maximizing the area enclosed by a given fence length, and minimizing the travel time of a swimmer who has to get to a point on the shore (relates to Snell's law).
Prof. Jason Starr
First Derivative Test, Critical and Extremal Points (lecture 9)
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PDF
Section 3, Page 4 to page 5
Max/Min problem of maximizing area enclosed by a trapezoid inscribed in a semicircle.
Prof. Jason Starr
Max/Min Problems (section 2 of lecture 10)
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PDF
Section 3, Page 3 to page 4
Problems and answers without full explanation. Finding tangent lines to an ellipse, minimizing surface area of a grain silo, finding the volume of a solid of revolution, computing an antiderivative using trig substitution, and computing an antiderivative using integration by parts.
Prof. Jason Starr
Tangent Lines (section 1 of lecture 2), Max/Min Problems (section 2 of lecture 10), Volume of Solids of Revolution (section 3 of lecture 19), Inverse Substitution (section 3 of lecture 25), Integration by Parts (section 1 of lecture 27)
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Online Textbook Chapters
Document
Definition of a critical point and its use in finding maxima and minima of a function.
Prof. Daniel J. Kleitman
Quadratic Approximations (OT10.1)
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Document
Finding the extremal values of a function, including distinction between local and global maxima and minima.
Prof. Daniel J. Kleitman
None
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Document
Iterative divide and conquer method for finding a local maximum or minimum on a curve.
Prof. Daniel J. Kleitman
Conditions for Maximum or Minimum (OT14.1)
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Practice Problem
PDF
Problem 2 (page 2)
An optimization problem involving two fixed rays and a segment that is allowed to slide between them.
Prof. Jason Starr
None
Solution (PDF) Pages 9 to 11
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Exam Questions
PDF
Problem 3 (page 6)
Finding the maximum volume of a box made from two square sheets of metal.
Prof. Jason Starr
None
Solution (PDF) Page 4
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PDF
Problem 5 (page 1)
Finding the maximum volume for a trash can made from a cylinder and a hemisphere.
Prof. Jason Starr
None
Solution (PDF) Page 2
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PDF
Problem 3.1 (page 2) to problem 3.2 (page 2)
Two problems which involve minimizing the cost of a sculpture and maximizing the area enclosed by a fence.
Prof. Jason Starr
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PDF - 2.2 MB
Problem 2C-1 (page 13) to problem 2C-15 (page 15)
Fifteen optimization questions drawn from various applications including largest volume of a box, shortest length of fence for a barnyard, and the optimal fare for an airline.
Prof. David Jerison
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PDF
Problem 2D-1 (page 15) to problem 2D-7 (page 16)
Seven optimization questions which include finding the optimum attack angle for a plane and the best moment to add milk to a cup of coffee to keep it hot.
Prof. David Jerison
None
Solution (PDF)# Page 28
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PDF
Problem 3 (page 1) to problem 4 (page 1)
Two questions which involve minimizing the area of a triangle and minimizing the length of wire needed to brace the legs of a table.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 2 (page 1)
Minimizing the material required to make a popcorn container.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 3 (page 1)
Finding the maximum area of a triangular enclosure formed from two sides of fence and a wall for the third side.
Prof. David Jerison
None
Solution (PDF)# Page 1
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PDF
Problem 6 (page 1)
Finding the largest possible area of a rectangle with two corners that lie on a given parabola.
Prof. David Jerison
None
Solution (PDF)# Page 1
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