Agenda and Assignments

Basic Mathematics for Social Scientists

Sections below (for the first half of the course) refer to [HC]. You are strongly encouraged to work on all the problems of the sections that we cover; solutions to these problems will become available over time, so that you could compare them with yours and consolidate your understanding. The suggested homework problems below are only a selection.

• Mon, Sept 15
  review of basic algebra, functions and graphs
  

• Wed, Sept 17
  review (continued); refreshing quiz (not for credit)
  

• Fri, Sept 19
  rates of change
  Section 2.1. #1, 3, 5, 6, 9, 14, 15, 17, 21
  Solutions

• Mon, Sept 22
  derivatives (concept)
  Section 2.2. #9-12, 14, 17, 30
  Section 2.3. #2, 8, 9, 17, 21, 24, 30
  Solutions

• Wed, Sept 24
  how to differentiate
  Section 3.1. #16, 23, 27, 34, 37, 45, 59
  Section 3.2. #2, 11, 15, 18, 25, 26, 29
  Solutions

• Fri, Sept 26
  chain rule
  Section 3.3. #1, 7, 12, 16, 21, 33, 34, 36, 41, 43, 48, 49
  Solutions

• Mon, Sept 29
  product rule; quiz
  Section 3.4. #5, 7, 13, 22, 23, 24, 40, 44
  Solutions
  Extra problem. Find the derivative of the following function.
  

• Wed, Oct 1
  marginal revenue and cost
  Section 2.5. #3, 4, 7, 8, 10, 14
  Solutions
  Section 3.2. #30
  Section 3.3. #40
  See links further above for solutions for these sections.

• Fri, Oct 3
  finding maxima and minima
  Section 4.1. #7, 8, 12, 16, 19
  Section 4.3. #3, 8, 15, 24, 32, 36, 39, 40
  (You may also attempt problems from sections 2.4 and 4.4 suggested below.)
  Solutions

• Mon, Oct 6
  second derivatives and inflection points
  Section 2.4. #1, 6-8, 10, 13, 15, 21-23, 25, 27, 29
  Solutions
  Section 4.2. #4, 12, 19, 24, 31, 33
  Look for this section's solutions in the links above.

• Wed, Oct 8
  more examples and word problems
  Section 4.4. #16, 20, 26
  Look for this section's solutions in the links above.
  Section 4.5. #8, 9
  Section 4.7. #2, 4, 10
  Section 4.8. #1
  Solutions

• Fri, Oct 10
  first test covering differentiation
  The test will take 50 minutes. Having a graphing calculator could be quite helpful.

  ---

• Wed, Oct 15
  summation and integration
  Section 5.1. #1, 4, 6, 8, 10, 16, 17, 19, 20
  Solutions

• Fri, Oct 17
  definite integral
  Section 5.2. #2, 5, 8, 12, 17
  Section 5.3. #1, 9, 11-16, 18, 27
  Solutions

• Mon, Oct 20
  interpretation of definite integral
  Section 5.4. #8-10, 15, 17
  Solutions
  Section 6.1. #1, 11
  Section 6.2. #3, 4, 6, 12
  Solutions

• Wed, Oct 22
  fundamental theorem of calculus; quiz
  Section 5.5. #3, 4, 9-13
  Solutions

• Fri, Oct 24
  finding anti-derivatives
  Section 7.1. #1, 10, 14, 16, 21-23, 32, 46, 47, 49, 54, 58, 61, 63, 65, 68
  Solutions

• Mon, Oct 27
  integration by substitution
  Section 7.2. #1, 3, 5-7, 17, 19-21, 23, 32, 33, 36, 38, 40, 42
  Section 7.3. #11, 16, 19, 21, 23, 25, 29, 36
  Solutions

• Wed, Oct 29
  integration by parts
  Review examples in class.
  short note and extra exercises

• Fri, Oct 31
  second test covering integration
  The test will take 50 minutes. Having a graphing calculator could be quite helpful.

  ---

  Sections below (for the rest of the course) refer to [L]. You are strongly encouraged to work on all the problems of the sections that we cover; the suggested homework problems below are only a selection. At the end of each section we cover, there are Practice Problems (with solutions) which could be a great starting point before attempting homework. The *-ed problems are for further work and are well recommended. Solutions will be posted here over time.

• Mon, Nov 3
  systems of linear equations
  Section 1.1. #2, 3, 5, 7, 8, 13, 17, 18, 20, 22, 24, 27, 31, 33*, 34*

• Wed, Nov 5
  row reduction and echelon forms
  Section 1.2. #1, 4, 6, 8, 11, 12, 16, 19, 23, 29, 31

• Fri, Nov 7
  vectors and matrices
  Section 1.3. #1, 3, 7, 9, 11, 17, 16, 20, 22, 26, 27, 29*, 32

• Mon, Nov 10
  matrix equations
  Section 1.4. #1, 3, 11, 13, 15, 18, 25, 26, 31, 32, 39, 41

• Wed, Nov 12
  homogeneous equations and linear independence
  Section 1.5. #3, 5, 15, 7, 17, 19, 21, 24, 25*, 27*, 33, 35
  Section 1.7. #1-3, 9, 15, 19, 22-29, 31, 33, 41, 43

• Fri, Nov 14
  linear transformations
  Section 1.8. #5, 7, 9, 11, 16-20, 32, 33, 38, 39, 24*, 25*, 30*, 31*,
  The following homework problems will be collected on Friday and will be graded as a quiz.
  Section 1.4, #39, 41; Section 1.5, #7; Section 1.7, #9.

• Mon, Nov 17
  linear transformations and matrices (continued)
  Section 1.9. #1, 6, 8, 15, 18, 22, 27, 31, 32, 35, 36*, 38, 39

• Wed, Nov 19
  matrix operations and inverses
  Section 2.1. #2, 7, 10-12, 20, 22*, 23, 24, 25*, 26*

• Fri, Nov 21
  inverse matrices (continued)
  Section 2.2. #7, 9, 10, 13, 17-22, 24*, 31, 32, 35, 37*

• Mon, Nov 24
  nullity and rank
  Section 2.8. #1-4, 6, 7, 9, 14, 18-22, 25, 27, 28, 33, 35
  Section 2.9. #11, 14, 16, 19, 24
  The following homework problems will be collected on Monday and will be graded as a quiz.
  Section 1.9, #39; Section 2.1, #12, 23; Section 2.2, #35.

• Wed, Nov 26
  determinants
  Section 3.1. #3, 13, 15, 21, 25, 30, 34, 37, 38*, 40, 41
  Section 3.2. #4, 5, 18, 21, 25, 27-29, 31, 34, 35

• Mon, Dec 1
  vector spaces
  Section 4.1. #1, 2, 5-8, 11, 21, 22, 23 (a-d)
  Section 4.2. #1, 3, 7, 11, 13, 15, 23, 25, 26 (a-e), 27, 28, 30*, 31*, 32*, 34*

• Wed, Dec 3
  vectors and bases
  Section 2.9. #1, 3, 6, 17, 18, 29, 30

• Fri, Dec 5
  base change, quiz
  Section 4.7. #1, 3, 5, 8, 12, 13, 14

• Mon, Dec 8
  eigenvalues and eigenvectors
  Section 5.1. #1, 2, 5, 6, 7, 11, 12, 14

• Wed, Dec 10
  eigenvalues (continued)
  Section 5.1. #17, 19, 20, 21 (except d), 22 (except c), 23, 24, 25*, 26*, 29*, 32
  Section 5.2. #1, 6, 9, 16, 18, 19, 21, 22, 24

• Fri, Dec 12
  using eigenvectors for diagonalization, quiz
  Section 5.3. #1, 3, 5, 7, 10, 11, 21, 22, 30, 31*, 32.
  Solutions to quiz 6

• Mon, Dec 15
  review

---