Purdue Calumet
MA 26100
Multivariate Calculus
Spring, 2015

Professor Roger Kraft
Office: Classroom Office Building, Room 368
Office phone: (219) 989-2696
Office hours: 2:00--4:00 MW, after class, and by appointment.
E-mail: roger@purduecal.edu

This page documents what we do in class. It contains reading and homework assignments from our textbook, and links to illustrations, demonstration programs, or other sources of information.

Monday, April 27. There will not be a quiz this Wednesday. The final exam will be Wednesday, May 6, at 6:00pm. Study for the final exam by making sure that you can solve all the problems from the three midterm exams and the 10 quizzes. Also, look at the review problems at the end of each chapter that were assigned for each midterm exam. Here are review sheets of what we have covered this semester. MA26100-Chapter13-Review.pdf MA26100-Chapter12-Review.pdf MA26100-Chapter11-Review.pdf Gradient Vector & Directional Derivatives.pdf Tangent Plane & Gradient Vector.pdf VectorAlgebra.pdf Here are two review sheets on integration from MA 16400. Indefinite integral Definite integral Wednesday, April 22. The quiz today is on Section 13.7. For Monday, read Sections 14.1 and 14.2. The homework problems for Section 13.8 are Section 13.8: 1, 3, 5, 7, 9, 15. If you would like to read some other explanations of triple integrals in cylindrical and spherical coordinates, try looking at the following references. Triple Integrals in Cylindrical Coordinates from Paul's CalcIII Notes Triple Integrals in Spherical Coordinates from Paul's CalcIII Notes Section 15.6 (PDF) from Calculus by David Guichard Triple Integrals in Spherical and Cylindrical Coordinates from Multivariable calculus at University of Minnesota Volume Element in Spherical and Cylindrical Coordinates from Multivariable Calculus: Early Integration Monday, April 20. The quiz on Wednesday is on Section 13.7. For Wednesday, read Section 13.8. The homework problems for Section 11.9 are Section 11.9: 3, 4, 5, 6, 9, 17, 19, 21, 23, 29. If you would like to read some other explanations of cylindrical and spherical coordinates, try looking at the following references. Cylindrical Coordinates from Paul's CalcIII Notes Spherical Coordinates from Paul's CalcIII Notes Section 12.6 Other Coordinate Systems (PDF) from Calculus Section 1.7 Curvilinear Coordinates from Vector Calculus, by Michael Corral Curvilinear Coordinates from Multivariable Calculus: Early Integration Wednesday, April 15. The quiz today is on Section 13.6. For Monday, read Section 11.9 (we need to cover Section 11.9 before we can cover Section 13.8) and Section 13.8. The homework problems for Section 13.7 are Section 13.7: 1, 3, 7, 9, 11, 13, 19, 21. If you would like to read some other explanations of triple integrals, try looking at the following references. Triple integrals from Kahn Academy Triple integrals from Paul's CalcIII Notes Triple integrals from Multivariable calculus at University of Minnesota The shadow method for triple integrals from Multivariable calculus The cross section method for triple integrals from Multivariable calculus Section 15.5 Triple Integrals (PDF) from Calculus by David Guichard Section 13.6 Triple Integration from APEX Calculus Section 3.3 Triple Integrals from Vector Calculus, by Michael Corral Monday, April 13. Today we will go over Section 13.6 The quiz Wednesday will be on Section 13.6. For Wednesday, read Section 13.7. The homework problems for Section 13.6 are Section 13.6: 1, 3, 5, 7, 9, 13. If you would like to read another explanation of the double integral for surface area, try looking at the following reference. Surface Area from Paul's CalcIII Notes Section 13.5 Surface Area from APEX Calculus Section 15.4 Surface Area (PDF) from Calculus Wednesday, April 8. Third midterm exam is today. For the Monday, read Section 13.6. Monday, April 6. The third exam will be this Wednesday, April 8. It will be on Sections 13.1, 13.2, 13.3, 13.4, 13.5, and Sections 10.5, 10.6. Here is a review sheet of what you should know for the exam. MA26100-Exam3-Review.pdf Here is a list of review problems, from the end of Chapter 13, that you should look at as you study for the exam. Section 13.10 Chapter Review: Sample Test Problems, pages 730-731: 1, 2, 3, 5, 6, 10, 12, 13. Wednesday, April 1. The quiz today is on polar coordinates (Sections 10.5 & 10.6) and Section 13.4. The homework problems for Section 13.5 are Section 13.5: 1, 3, 5, 7, 9, 15, 19. When you read Section 13.5, you may need to go back and review the material on moments and center of mass from Section 6.6. If you would like to read some other explanations of densities, moments, and center of mass, try looking at the following reference. Section 3.6 Application: Center of Mass from Vector Calculus Section 13.4 Center of Mass from APEX Calculus Section 15.3 Moment and Center of Mass (PDF) from Calculus Section 9.6 Center of Mass from Calculus Monday, March 30. The quiz Wednesday is on polar coordinates (Sections 10.5 & 10.6) and Section 13.4. For Wednesday, read Sections 13.5 an 13.6. The homework problems for Section 13.4 are Section 13.4: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23. If you would like to read some other explanations of double integrals in polar coordinates, try looking at the following references. Double Integrals in Polar Coordinates from Paul's CalcIII Notes Section 13.3 Double Integration with Polar Coordinates from APEX Calculus Double Integrals in Rectangular and Polar Coordinates Section 3.5 Change of Variables in Multiple Integrals from Vector Calculus Section 14.2 from Calculus, by Gilbert Strang Wednesday, March 25. The quiz today is on Section 13.3. Today and Monday we will go over polar coordinates. Monday, March 23. The quiz Wednesday is on Section 13.3. For Wednesday, read Section 13.4. When you read Section 13.4, you may need to go back and review the material on polar coordinates from Sections 10.5, 10.6, and 10.7. The following pages review polar coordinates and area in polar coordinates (what our textbook covers in Sections 10.5, 10.6, and 10.7). Points of Special Interest on the Unit Circle Section 6.4 from Trigonometry, by Michael Corral Sections 9.4 & 9.5 from APEX Calculus Polar Coordinates from Math Insight.org Polar Coordinates from Paul's CalcII Notes Area with Polar Coordinates from Paul's CalcII Notes Polar Coordinates from Kahn Academy Area defined by polar graphs from Kahn Academy Wednesday, March 18. The quiz today is on Sections 13.1 and 13.2 The homework problems for Section 13.3 are Section 13.3: 3, 5, 7, 11, 13, 15, 19, 25, 33, 35, 37, 43. If you would like to read some other explanations of non-rectangular regions of integration, try looking at the following references. Double Integral 5 from Khan Academy Double Integrals Over General Regions from Paul's CalcIII Notes Examples of changing the order of integration from Math Insight Double integrals where one integration order is easier from Math Insight Section 3.2 Double Integrals Over a General Region from Vector Calculus Section 13.1 Iterated Integrals and Area from APEX Calculus Section 13.2 Double Integration and Volume from APEX Calculus Monday, March 16. The quiz Wednesday is on Sections 13.1 and 13.2 For Wednesday, read Section 13.3. The homework problems for Section 13.1 are Section 13.1: 1, 3, 5, 7, 8, 9, 15, 17, 19. If you would like to read some other explanations of double integrals, try looking at the following references. Double Integrals from Paul's CalcIII Notes Introduction to double integrals from Math Insight The homework problems for Section 13.2 are Section 13.2: 1, 3, 5, 7, 9, 13, 17, 19, 23, 25. If you would like to read some other explanations of iterated integrals, try looking at the following references. Double Integral 1 from Khan Academy Iterated Integrals from Paul's CalcIII Notes Double Integrals from Oregon State University Double integrals as iterated integrals from Math Insight Section 3.1 Double Integrals from Vector Calculus Section 15.1 Volume and Average Height (PDF) from Calculus Wednesday, March 11. Spring break. Monday, March 9. Spring break. Wednesday, March 4. Second midterm exam is today. For the Monday after Spring Break, read Sections 13.1 and 13.2. Monday, March 2. The second exam will be this Wednesday, March 4. It will be on Section 11.8, and Chapter 12, Sections 12.1, 12.2, 12.4, 12.5, 12.6, 12.7, and 12.8. Here is a review sheet of what you should know for the exam. MA26100-Exam2-Review.pdf These are slightly more detailed summaries of tangent plane, gradient, and directional derivatives. Tangent Plane & Gradient Vector.pdf Gradient Vector & Directional Derivatives.pdf Here is a list of review problems, from the end of Chapter 12, that you should look at as you study for the exam. Section 12.10 Chapter Review, page 675: 2, 3, 5, 7, 9, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 26. The homework problems for Section 12.7 are Section 12.7: 1, 3, 5, 7, 9, 11, 13, 15, 16. If you would like to read some other explanations of tangent plane approximations, try looking at the following references. Tangent Planes and Linear Approximations from Paul's CalcIII Notes Gradient Vector and Tangent Planes from Paul's CalcIII Notes The homework problems for Section 12.8 are Section 12.8: 1, 3, 5, 7, 9. If you would like to read some other explanations of maximums and minimums, try looking at the following references. Absolute Minimums and Maximums from Paul's CalcIII Notes Introduction to local extrema of functions of two variables from Multivariable calculus at University of Minnesota Section 2.5 from Vector Calculus, by Michael Corral Wednesday, February 25. The quiz today is on Sections 12.4 and 12.5. For Monday, read Sections 12.7 and 12.8. The second exam will be next Wednesday, March 4. It will be on Section 11.8, and Chapter 12, Sections 12.1, 12.2, 12.4, 12.5, 12.6, 12.7, and 12.8. More detailed review information will be here in a couple of days. Here is another explanation of the material from Section 12.5. Gradient Vector & Directional Derivatives.pdf The homework problems for Section 12.6 are Section 12.6: 1, 3, 5, 7, 9, 13, 15, 16. If you would like to read some other explanations of the chain rule, try looking at the following references. Chain Rule from Paul's CalcIII Notes Section 13.5 from Calculus, by Gilbert Strang Monday, February 23. The quiz on Wednesday will be on Sections 12.4 and 12.5. For Wednesday, read Section 12.6. The homework problems for Section 12.5 are Section 12.5: 1, 3, 5, 9, 11, 13, 15, 23, 25. If you would like to read some other explanations of directional derivatives, try looking at the following references. Gradient from Khan Academy Directional Derivatives from Paul's CalcIII Notes Gradient Vector and Tangent Planes from Paul's CalcIII Notes Section 2.4 from Vector Calculus, by Michael Corral Section 14.5 Directional Derivatives (PDF) from Calculus Wednesday, February 18. For Monday, read Section 12.5. The homework problems for Section 12.4 are Section 12.4: 1, 3, 5, 9, 11, 13, 17. Here is a summary of the material from Section 12.4. Tangent Plane & Gradient Vector.pdf If you would like to read some other explanations of the tangent plane, try looking at the following references. Section 2.3 from Vector Calculus, by Michael Corral Tangent Planes from Paul's CalcIII Notes Monday, February 16. The quiz Wednesday will be on Sections 12.1 and 12.2. Today we will go over Section 12.2. For Wednesday, read Section 12.4 (we shall skip Section 12.3). Here are a few online programs for graphing functions z=f(x,y) along with their level sets (horizontal cross sections) and partial derivatives (vertical cross sections). Google's 3D Graphing Calculator GraphyCalc - 3d Graphing Calculator Contour Diagram and 3D Function Grapher (Description) Functions of Two Variables from M.I.T. CalcPlot3D: Multivariable Calculus Exploration Applet Wednesday, February 11. The quiz today is on Section 11.8. Today we will finish Section 12.1. The homework problems for Section 12.2 are Section 12.2: 1, 3, 5, 7, 9, 11, 13, 17, 19, 25, 27, 29, 37, 38, 39. If you would like to read some other explanations of partial derivatives, try looking at the following reference. Partial Derivatives from Khan Academy Partial Derivatives from Paul's CalcIII Notes Interpretations of Partial Derivatives from Paul's CalcIII Notes Introduction to partial derivatives from University of Minnesota Higher Order Partial Derivatives from Paul's CalcIII Notes Section 2.2 Partial Derivatives from Vector Calculus, by Michael Corral Section 14.3 Partial Differentiation (PDF) from Calculus Monday, February 9. The quiz Wednesday will be on Section 11.8 For Wednesday, read Section 12.2. The homework problems for Section 11.8 are Section 11.8: 1, 3, 5, 9, 11, 15, 17, 18, 19. The homework problems for Section 12.1 are Section 12.1: 1, 5, 6, 7, 8, 9, 10, 17, 19, 23, 25, 26. If you would like to read some other explanations of quadric surfaces, try looking at the following references. Quadric Surfaces from Paul's CalcIII Notes Quadric surfaces from University of Minnesota Section 1.6 from Vector Calculus, by Michael Corral Interactive Gallery of Quadric Surfaces If you would like to read some other explanations of functions of two variables, try looking at the following references. Surfaces as graphs of functions from University of Minnesota Functions of Several Variables from Paul's CalcIII Notes Contour Diagram and 3D Function Grapher from Multivariable Calculus Applets Wednesday, February 4. First midterm exam is today. For Monday, read Sections 11.8 (and skip Section 11.7) and 12.1. Monday, February 2. Remember that the first midterm exam is this Wednesday. See the review material below. Today we will finish Sections 11.5 and 11.6. The homework problems for Section 11.6 are Section 11.6: 1, 3, 5, 9, 13, 17, 19, 23, 25. NOTE: When solving these problems, don't write the "symmetric equations" of a line, always write the "parametric equations". If you would like to read some other explanations of the parametric equations for a line, try looking at the following references. Parametric representations of lines from Kahn Academy Parametrization of a line from University of Minnesota Tangent lines to parametrized curves from University of Minnesota Equations of Lines from Paul's CalcIII Notes Section 1.5 Lines and Planes from Vector Calculus, by Michael Corral Section 12.5 Lines and Planes (PDF) from Calculus Wednesday, January 28. The quiz today is on Sections 11.3 and 11.4. For Monday, read Section 11.6. Remember that the first midterm exam is next Wednesday. Here is a review sheet of what you should know for the exam. MA26100-Exam1-Review.pdf Review this summary of all the vector algebra rules from Sections 11.2, 11.3, and 11.4. VectorAlgebra.pdf Here is a list of review problems that you should look at as you study for the exam, which will be on Chapter 11, Sections 11.1, 11.2, 11.3, 11.4, 11.5, 11.6. Section 11.10 Chapter Review, pages 616-617: 1, 2, 3, 5, 6, 7c, 9, 11, 12a, 15, 19, 23, 27, 31, 33, 35, 37. Monday, January 26. The quiz Wednesday will be on Sections 11.3 and 11.4. The homework problems for Section 11.5 (pages 581-587 and skip the optional section on Kepler's Laws) are Section 11.5: 9, 13, 14, 15, 17, 19, 27, 33, 35, 39, 43. If you would like to read some other explanations of parametric curves, try looking at the following references. Parametric Equations from Khan Academy An introduction to parametrized curves from University of Minnesota Parametric Equations and Curves from Paul's CalcII Notes Vector Functions from Paul's CalcIII Notes Calculus with Vector Functions from Paul's CalcIII Notes Arc Length with Vector Functions from Paul's CalcIII Notes Sections 1.8 and 1.9 from Vector Calculus, by Michael Corral Wednesday, January 21. For Monday, read Section 11.5 (pages 581-587 and skip the optional section on Kepler's Laws). In order to really understand Section 11.5, you will need to review a few previous sections from the textbook: Section 6.4 (pages 342-346), Section 10.4 (pages 532-536), and Section 11.1 (pages 560-561). Here is a summary of all the vector algebra rules from Sections 11.2, 11.3, and 11.4. VectorAlgebra.pdf The homework problems for Section 11.4 are Section 11.4: 1, 3, 5, 7, 9, 11, 13, 15, 23, 25, 27. If you would like to read some other explanations of the cross product, try looking at the following references. Cross Product from Kahn Academy Cross Product from University of Minnesota Cross Product from Paul's CalcII Notes Sections 1.4 and 1.5 from Vector Calculus, by Michael Corral Section 12.4 The Cross Product (PDF) from Calculus Monday, January 19. No class today. Wednesday, January 14. The quiz today is on Sections 11.1 and 11.2. For next Wednesday, read Section 11.4. Today we will start Section 11.3. The homework problems for Section 11.3 are Section 11.3: 5, 11, 13, 14, 17, 19, 23, 25, 43, 44, 65, 71. If you would like to read some other explanations of the dot product, try looking at the following references. Section 1.3 Dot Product from Vector Calculus, by Michael Corral Dot Product from Paul's CalcII Notes Dot Product from University of Minnesota Equations of Planes from Paul's CalcIII Notes Defining a plane in R3 with a point and normal vector from Kahn Academy Section 12.3 The Dot Product (PDF) from Calculus Monday, January 12. The first quiz will be Wednesday on Sections 11.1 and 11.2. For Wednesday, read Section 11.3. Today we will cover Sections 11.1 and 11.2. The homework problems for Section 11.1 are Section 11.1: 1, 3, 5, 8, 9, 10, 11, 13, 21, 37, 39, 41. The homework problems for Section 11.2 are Section 11.2: 1, 5, 6, 9, 15, 17, 19. If you would like to read some other explanations of 3D Cartesian coordinates, try looking at the following references. Real coordinate spaces from Kahn Academy The 3-D Coordinate System from Paul's CalcIII Notes 3D Coordinate Systems by Philippe B. Laval Section 1.1 from Vector Calculus, by Michael Corral If you would like to read some other explanations of vectors, try looking at the following references. Vectors from Kahn Academy Vectors from Kahn Academy Vectors from Paul's CalcII Notes Maths Help...working with vectors Section 1.2 from Vector Calculus, by Michael Corral