MTH 255
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Homework
All homework will be found in the textbook, James Stewart’s Calculus: Concepts and Contexts, 4th Edition. Select prompts for each section of homework are listed below.
The homework prompts listed are a starting point to practice the material we learned in class (or from the videos). Some people may feel they need more practice after working through these prompts, and that is great to have that self-awareness! In this case, try some of the even prompts between the assigned odd ones.
Strang and Herman’s Calculus Volume 3
- Cylindrical & Spherical Coordinates: Section 2.7: 363 – 371 all, 379, 385 – 393 all, 401, 411, 413
- Parametric Surfaces: Section 6.6: 273 – 278 all, then do these exercises.
- Lagrange Multipliers: Section 4.8: 359, 361, 365 – 373 odd, 381, 385, 389
- Surface Area: Do these exercises.
- Triple Integrals: Section 5.4: 181, 187, 189 (do not do this prompt; just take note of the statement), 191, 195, 197, 199, 205, 211, 219, 221
- Triple Integrals in Other Coordinates: Section 5.5: 241, 245, 249, 255, 259, 267, 269, 271, 277, 281, 283, 285
- The Jacobian: Section 5.7: 257, 261, 369, 379, 381, 387, 391, 393, 395, 397
- Vector Fields: Section 6.1: 5 (by hand), 7 (by hand), 9 (by hand), 15, 17, 19, 32 – 38 all
- Line Integrals: Section 6.2: 41, 43, 55, 56, 57, 58, 67 (Work is integrating F⋅dr), 69
- The Fundamental Theorem of Line Integrals: Section 6.3: 101, 103, 107, 111, 115, 119, 123, 131
- Green’s Theorem: Section 6.4: 147, 151, 153, 157, 159, 165, 171, 185
- Curl: Section 6.5: 207, 209, 211, 213, 217, 219, 239, 251, 253
- Divergence: Section 6.5: 223, 225, 231, 235, 237, 245, 247, 249
- Surface Integrals & Flux: Section 6.6: Surface Integrals: 281, 283, 291, 295, ; Flux: 285, 303, 304, 305
- Stokes’ Theorem: Section 6.7: 327, 331, 333, 335, 339, 345, 353
- The Divergence Theorem: Section 6.8: 385, 387, 391, 393, 403, 405
- Applications:
Stewart’s Calculus: Concepts & Contexts, 4th Edition 
- Cylindrical & Spherical Coordinates: §9.7 (p. 686): # 3, 5, 7, 9, 11, 12, 13, 14, 15, 17, 25, 27, 29
- Parametric Surfaces: §10.5 (p. 731): # 1, 3, 5, 7 — 11 odd, 13 — 18 all, 19 — 23 odd, 27, 29
- Lagrange Multipliers: §11.8 (p. 818): # 3, 5, 7, 9, 19, 27, 29
- Surface Area: §12.6 (p. 871): # 1 — 13 odd, 15a, 20abc, 21, 25
- Triple Integrals: §12.7 (p. 880): # 3 — 15 odd, 19, 21, 27 — 33 odd, 35
- Triple Integrals in Cylindrical & Spherical Coordinates: §12.8 (p. 887): # 3, 5, 7, 11, 17, 19, 35, 37
- The Jacobian: §12.9 (p. 898): # 5 — 19 odd, 25
- Vector Fields: §13.1 (p. 911): # 5, 9, 13, 17, 19, 21, 25, 27, 29, 31
- Line Integrals: §13.2 (p. 922): # 3, 7, 11, 15, 17, 21, 25, 41
- The Fundamental Theorem of Line Integrals: §13.3 (p. 932): # 1, 5, 9, 11, 13, 17, 19, 21, 25, 33
- Green’s Theorem: §13.4 (p. 939): # 3, 5, 7, 11, 13, 17, 21, 23
- Curl & Divergence: §13.5 (p. 947): # 1, 3, 7, 11, 12, 13, 17, 21, 25, 37
- Surface Integrals & Flux: §13.6 (p. 959): # 3, 5, 7, 11, 15, 17, 19, 21, 25, 29
- Stokes’ Theorem: §13.7 (p. 965): # 1, 3, 7, 9, 11, 15, 17, 19
- The Divergence Theorem: §13.8 (p. 971): # 1, 3, 5, 7, 9, 11, 13, 19
- Applications: §13.4: # 22, 23, 24; then §13.6: # 37 – 46 all; then §13.8: # 20, 23
Note Sheets
Below are a number of Guided Note Sheets. These are blank and constitute what will be covered during lecture.
- Prerequisite Topics
- §9.7: Cylindrical & Spherical_Coordinate_Systems
- §10.5: Parametric Surfaces
- §11.8: Lagrange Multipliers
- §12.6: Surface Area
- §12.7: Triple Integrals
- §12.8: Triple Integrals in Cylindrical & Spherical_Coordinates
- §12.9: The Jacobian
- §13.1: Vector Fields
- §13.2: Line Integrals
- §13.3: The Fundamental Theorem of Line Integrals
- §13.4: Green’s Theorem
- §13.5: Curl & Divergence
- §13.6: Surface Integrals & Flux
- §13.7: Stokes’ Theorem
- §13.8: The Divergence Theorem
- §13.9: The Fundamental Theorems of Calculus
- Applications
Mini Tests
There are four Mini Tests to be completed through the term. You may find them below.
- Mini Test 1 (covers §9.7, 10.5, 11.8)
- Mini Test 2 (covers §12.6 – 12.8)
- Mini Test 3 (covers §12.9 – 13.3)
- Mini Test 4 (covers §13.4 – 13.8)
Reviews
Below are some reviews for both the midterm exam and the final exam. Use these reviews to study for the exam. These will not be collected or covered in class.
- Review for Midterm Exam (covers §9.7 – 12.9)
- Review for Final Exam (cumulative, focusing on Chapter 13)
Extra Credits
There are two extra credit opportunities available to you. Please complete these any time before the last week of instruction.
- Extra Credit 1: Women in Math: The Limit Does Not Exist
- Extra Credit 2: The Mathematics of the Three Waves of AI