MTH 255
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Homework
All homework will be found in the textbook, James 厂迟别飞补谤迟’蝉听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聽Calculus Volume 3
- Cylindrical & Spherical Coordinates: : 363 – 371 all, 379, 385 – 393 all, 401, 411, 413
- Parametric Surfaces: : 273 – 278 all, then do these exercises.
- Lagrange Multipliers: : 359, 361, 365 – 373 odd, 381, 385, 389
- Surface Area: Do these exercises.
- Triple Integrals: : 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: : 241, 245, 249, 255, 259, 267, 269, 271, 277, 281, 283, 285
- The Jacobian: : 257, 261, 369, 379, 381, 387, 391, 393, 395, 397
- Vector Fields: : 5 (by hand), 7 (by hand), 9 (by hand), 15, 17, 19, 32 – 38 all
- Line Integrals: : 41, 43, 55, 56, 57, 58, 67 (Work is integrating聽贵鈰�dr), 69
- The Fundamental Theorem of Line Integrals: : 101, 103, 107, 111, 115, 119, 123, 131
- Green’s Theorem: : 147, 151, 153, 157, 159, 165, 171, 185
- Curl: : 207, 209, 211, 213, 217, 219, 239, 251, 253
- Divergence: : 223, 225, 231, 235, 237, 245, 247, 249
- Surface Integrals & Flux: : Surface Integrals: 281, 283, 291, 295, ; Flux: 285, 303, 304, 305
- Stokes’ Theorem: : 327, 331, 333, 335, 339, 345, 353
- The Divergence Theorem: : 385, 387, 391, 393, 403, 405
- 础辫辫濒颈肠补迟颈辞苍蝉:听
厂迟别飞补谤迟’蝉听Calculus: Concepts & Contexts, 4th Edition 
- Cylindrical & Spherical Coordinates: 搂9.7 (p. 686): # 3, 5, 7, 9, 11, 12, 13, 14, 15, 17, 25, 27, 29
- Parametric Surfaces: 搂10.5 (p. 731): # 1, 3, 5, 7 — 11 odd, 13 — 18 all, 19 — 23 odd, 27, 29
- Lagrange Multipliers: 搂11.8 (p. 818): # 3, 5, 7, 9, 19, 27, 29
- Surface Area: 搂12.6 (p. 871): # 1 — 13 odd, 15a, 20abc, 21, 25
- Triple Integrals: 搂12.7 (p. 880): # 3 — 15 odd, 19, 21, 27 — 33 odd, 35
- Triple Integrals in Cylindrical & Spherical Coordinates: 搂12.8 (p. 887): # 3, 5, 7, 11, 17, 19, 35, 37
- The Jacobian: 搂12.9 (p. 898): # 5 — 19 odd, 25
- Vector Fields: 搂13.1 (p. 911): # 5, 9, 13, 17, 19, 21, 25, 27, 29, 31
- Line Integrals: 搂13.2 (p. 922): # 3, 7, 11, 15, 17, 21, 25, 41
- The Fundamental Theorem of Line Integrals: 搂13.3 (p. 932): # 1, 5, 9, 11, 13, 17, 19, 21, 25, 33
- Green’s Theorem: 搂13.4 (p. 939): # 3, 5, 7, 11, 13, 17, 21, 23
- Curl & Divergence: 搂13.5 (p. 947): # 1, 3, 7, 11, 12, 13, 17, 21, 25, 37
- Surface Integrals & Flux: 搂13.6 (p. 959): # 3, 5, 7, 11, 15, 17, 19, 21, 25, 29
- Stokes’ Theorem: 搂13.7 (p. 965): # 1, 3, 7, 9, 11, 15, 17, 19
- The Divergence Theorem: 搂13.8 (p. 971): # 1, 3, 5, 7, 9, 11, 13, 19
- Applications: 搂13.4: # 22, 23, 24; then 搂13.6: # 37 – 46 all; then 搂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
- 搂9.7: Cylindrical & Spherical_Coordinate_Systems
- 搂10.5: Parametric Surfaces
- 搂11.8: Lagrange Multipliers
- 搂12.6: Surface Area
- 搂12.7: Triple Integrals
- 搂12.8: Triple Integrals in Cylindrical & Spherical_Coordinates
- 搂12.9: The Jacobian
- 搂13.1: Vector Fields
- 搂13.2: Line Integrals
- 搂13.3: The Fundamental Theorem of Line Integrals
- 搂13.4: Green’s Theorem
- 搂13.5: Curl & Divergence
- 搂13.6: Surface Integrals & Flux
- 搂13.7: Stokes’ Theorem
- 搂13.8: The Divergence Theorem
- 搂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 搂9.7, 10.5, 11.8)
- Mini Test 2 (covers 搂12.6 – 12.8)
- Mini Test 3 (covers 搂12.9 – 13.3)
- Mini Test 4 (covers 搂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 搂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