Portland Community College | Portland, Oregon

MTH 253

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Homework

There are two different textbook options you may choose in order to complete your homework. You may choose either

• Gilbert Strang and Edwin Herman’s Calculus Volume 1 and Calculus Volume 2
• James Stewart’s Calculus: Concepts and Contexts, 4th Edition

Select homework sets are provided below for either option you choose. 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 1 and Calculus Volume 2

Volume 1

• Linear Approximations & Differentials: Section 4.2: 51 – 61 odd, 69 – 83 odd
• Newton’s Method: Section 4.9: 409, 411, 415, 417, 419, 423, 425, 427, 431, 453

Volume 2

• Introduction to Differential Equations: Section 4.1: 1, 3, 9, 13, 17, 19, 21, 25, 31, 33, 39, 41
• Slope Fields: Section 4.2: 66 – 73 all, 75, 77, 81, 83, 84 – 88 all, 114, 115
• Separable Equations: Section 4.3: 119, 121, 123, 125, 127, 131, 133, 135, 139, 141, 149
• Newton’s Law of Cooling: Section 4.3: 156 – 162 all
• Sequences: Section 5.1: 1, 3, 9, 13, 15, 19, 21, 23, 27 – 29 odd, 45 – 57 odd
• Series: Section 5.2: 67, 69, 71, 73, 79, 81, 89 – 97 odd, 102, 103, 106
• Integral Test: Section 5.3: 139, 141, 147, 153, 155, 159, 161, 169, 171
• Comparison Tests: Section 5.4: 194 – 200 all, 207 – 211 all
• Alternating Series Test: Section 5.5: 250 – 255 all, 264, 295, 297, 303, 304
• Ratio Test: Section 5.6: 317 – 323 odd, 349 (note the denominator factors as (n + 1)^3)
• Power Series: Section 6.1: 5, 7, 9, 11, 13 – 21 all, 25, 31
• Power Series Representation: Section 6.2: Begin with Section 6.1: 33, 35, 37, 39, then do Section 6.2: 65, 69, 70, 87, 89, 95, 97, 99, 109 (Why do you think it is called E(x)?)
• Taylor & Maclaurin Series: Section 6.4: 174, 175, 177, 203, 205, 207; then Section 6.3: 141 – 159 odd
• Taylor Polynomials: Section 6.3: 116 – 123 all; then Section 6.4: 219, 221, 223
• Series Solutions to Differential Equations: Supplement: 1, 2, 3, 4

Stewart’s Calculus: Concepts & Contexts, 4th Edition

• Linear Approximations & Differentials: §3.9 (p. 245): # 1, 5 – 11 odd, 15, 17, 21 – 27 odd
• Newton’s Method: §4.7 (p. 315): # 1 – 17 odd, 25
• Introduction to Differential Equations: §7.1 (p. 498): # 1 – 13 odd
• Slope Fields: §7.2 (p. 506): # 1 – 13 odd
• Separable Equations: §7.3 (p. 514): # 1 – 21 odd
• Newton’s Law of Cooling: §7.4 (p. 527): # 13, 14, 15, 16
• Sequences: §8.1 (p. 562): # 5 – 25 odd, 31, 35, 37, 49, 51
• Series: §8.2 (p. 572): # 5 – 25 odd, 31, 33, 41
• Integral & Comparison Tests: §8.3 (p. 583): # 1 – 25 odd, 37
• Alternating Series Test & Ratio Test: §8.4 (p. 591): # 1 – 29 odd, 39
• Power Series: §8.5 (p. 597): # 3 – 23 odd
• Power Series Representation: §8.6 (p. 603): # 1 – 29 odd, 35
• Taylor & Maclaurin Series: §8.7 (p. 616): # 3, 7, 11, 13, 15, 19, 21, 23, 25, 27, 31, 35, 39, 43, 45, 59
• Taylor Polynomials: §8.8 (p. 625): # 1 – 7 odd, 11, 15, 19 — 27 odd
• Series Solutions to Differential Equations: §8.9 (Supplemental): # 1, 3, 5, 7

Note Sheets

Below are a number of Guided Note Sheets. These are blank and constitute what will be covered during lecture.

• Linear Approximations & Differentials
  
• Newton’s Method
• Modeling with Differential Equations
• Direction Fields
• Separable Equations
• Newton’s Law of Cooling
• Sequences
• Series
• Estimating a Sum
• The Comparison Tests
• The Integral Test & p-Series
• Absolute Convergence & the Ratio Test
• Alternating Series
• Power Series
• Representation of Functions as Power Series
• Taylor & Maclaurin Series
• Taylor’s Inequality
• Applications of Taylor Polynomials
• Series Solutions to DEs

Mini Tests

There are four Mini Tests to be completed through the term. You may find them below.

• Mini Test 1 (covers Volume 1 4.2 & 4.9 and Volume 2 4.1)
• Mini Test 2 (covers 4.2, 4.3, and 4.4)
• Mini Test 3 (covers 5.1, 5.2, and 5.3)
• Mini Test 4 (covers 5.4, 5.5, 5.6, 6.1, and 6.2)

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 Linear Approximations, Newton’s Method, and Differential Equations)
• Review for Final Exam (cumulative, focusing on Sequences & Series)
• Key for Final Review

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

Videos

• MTH 253 Videos: Austina Fong and myself have produced a video series for MTH 253. Feel free to check out her videos if you like.
• Updated MTH 253 Videos: Austina Fong independently made significantly shorter, updated videos to follow along with the OpenStax material.

Precalculus Review Materials

PCC has created a wealth of information for precalculus review. If you identify any topics you need assistance with, check this site out.