The final exam will be written Friday December 14, 1:30pm in Phillps Wangensteen 2-470. The exam will be common to all sections of Math1272 this semester, and will cover material from the entirety of the course.

The final exam is closed book. No external resources (including electronic devices such as calculators, cell phones, etc) may be used during the exam. However, a formula sheet will be provided with the exam    pdf

Professor Ames will hold his usual office hours (Mon 1-2 5-6, Tues 11-12) the week of the final exam, as well as additional office hours Wed 1-3, Thurs 2-4 and Fri 9-11. The TAs will hold their usual office hours the week of the final exam as well. Meetings outside of office hours can be arranged via email.
Please consult the course calendar for the complete schedule of office hours.

Follow this link for additional preparatory materials for the exam. You are also encouraged to review your own and the posted lecture notes, homework solutions, midterm solutions, etc.

Homework 11     pdf     solutions

Midterm III     pdf     solutions

Recent Lecture Notes:

Wed Dec 12: Equations of Lines and Planes (12.5), Review (Equation of plane example)
Mon Dec 10: Dot and Cross Product cont'd (12.3-12.5)
Fri Dec 7: Vectors, Dot Product (12.2, 12.3) (slides)
Wed Dec 5: Vectors (12.2) (slides)
Mon Dec 3: 3-Dimensional Coordinate Systems (12.1) (slides)

Week 1 (due Sept 11)    (pdf) (solutions)
7.7 2, 6, 20, 30. 7.1 8, 20, 32, 36, 38, 48.
Hint for problem 7.7.2: You need to use the Hermite-Hadamard inequality (given in the pdf) to finish part b.

Week 2 (due Sept 18)    (pdf) (solutions)
7.2 10, 18, 22, 32, 34, 42, 56. 7.3 6, 10, 16, 26, 32.
The following problems (previously assigned) will be included in HW3: 7.3 16, 26.
The following problems should be attempted for practice, but will not be graded: 7.2 18, 32. 7.3 32.

Week 3     (pdf) (solutions)
7.3 16, 26. 7.4 6, 16, 22, 50. 7.8 8, 12, 20.
Homework 3 will not be collected or graded and is meant as preparation for next week's midterm.

Week 4 (due Oct 4)    (pdf) (solutions)
7.4 2, 24, 48, (bonus: 30). 7.8 6, 14, 24, 34, 40, (bonus: 38).
Problems for extra practice (not to be handed in): 7.4 1,7, 9, 33, 37, 41, 45, 47, 51. 7.8 7, 11, 21, 23, 31, 33, 35.

Week 5 (due Oct 9)     (pdf) (solutions)
8.1 2, 34(a), 36, (bonus: 24). 8.4 4, 10, 16, 18 (bonus: 6).
Hints: for 8.1.36 use u-substitution and the formula for the integral given in the pdf. For 8.1.24 compare your approximate integral with the actual value 5.074094 (rounded to 6 decimal places).

Week 6 (due Oct 16)    (pdf) (solutions)
8.5 6, 10 9.1 2, 4. 9.3 6, 42 (46 bonus)
Problems for extra practice (not to be handed in): 8.5 3, 5, 7, 11, 19. 9.1 1, 3, 5, 7, 11, 13.
9.3 1 to 23 (odd), 33, 35, 39, 41, 43, 45, 47, 51.

Week 7     (pdf) (answers) (solutions)
9.5 2, 4, 16, 20, 23. 9.2 22, 24. 9.6 2. Homework 7 will not be collected or graded and is meant as preparation for next week's midterm.
Problems for extra practice: 9.5 1-19 (odd). 9.2 19, 21, 23. 9.6 1, 3, 5.

Week 9 (Due Nov 6)    (pdf) (solutions)
10.1 8. 10.2 28, 34, 42 10.3 6, 16, 26, 60 (bonus: 74) Problems for extra practice: 10.1 1-17 (odd), 31, 33, 41, 43, 45. 10.2 1-19 (odd), 27, 31, 33, 41, 43. 10.3 1-25 (odd), 49, 51, 61, 63.

Week 10 (Due Nov 13)    (pdf) (solutions)
10.4 14, 44, 46. 11.1 14, 18, 28, 34, 46, 82 (bonus: 70).
Problem 10.4.44: set up the integral you would evaluate to find the area but don't solve it.
Problems for extra practice: 10.4 1-42, 45-49 (odd) 11.1 13-55, 65, 73-81 (odd).

Week 11 (Due Nov 20)    (pdf) (solutions)
11.2 4, 22, 30. 11.3 32, 34. 11.4 10, 18 (bonus 40). 11.5 6, 32. 11.6 4, 6, 20.
Problems for extra practice: 11.2 15-41, 49-63. 11.3 1-31. 11.4 1-31. 11.5 1-19, 33. 11.6 1-37.

Week 13 (Due Dec 6)     (pdf) (solutions)
11.8 40, 42. 11.10 6, 10, 18, 20, 48, 64, 74 (Bonus).
Problems for extra practice: 11.8 3-28. 11.10 1-57, 63-75.

Midterm III was held November 27 during discussion.     pdf     solutions
The midterm covered material from Sections 10.1-10.4 and 11.1-11.8 in the text.
Two sample midterms are available:     Sample 3a (sols)     Sample 3b (sols)

Midterm II was held October 25 during discussion.     pdf     solutions
The midterm covered the material from Sections 8.1, 8.4, 8.5, 9.1, 9.2, 9.3, 9.5, 9.6 presented in class. Two sample midterms are available here:  Sample 2a (Solutions)   Sample 2b (Solutions)

Midterm I was held September 27 in discussion.     pdf     solutions
The midterm covered material from Chapter 7 in the text.
Two sample midterms are available here:     Sample 1A (solutions)     Sample 1B (solutions)

Lecture 1, Sept 5: Approximate Integrals (7.7)
(syllabus slides) (lecture slides) (examples)

Lecture 2, Sept 7: Error bounds, Simpson's rule (7.7), and Integration by parts (7.1)
(slides) (Integration by parts example)

Lecture 3, Sept 10: Integration by parts and Integration of trigonometric functions (7.1,7.2)
(slides) (IBP examples) (HH inequality notes)

Lecture 4, Sept 12: Trigonometric integration and substitution (7.2, 7.3)
(slides) (examples)

Lecture 5, Sept 14: Trigonometric substitution (7.3)
(slides) (examples)

Lecture 6, Sept 17: More trig substition and Integration by partial fractions (7.4)
(slides) (Trig substitution examples)

Lecture 7, Sept 19: Integration of rational functions by partial fractions (continued) (7.4)
(slides)

Lecture 8, Sept 21: Integration of rational functions by partial fractions (conclusion) (7.4) and Improper Integrals (7.8) (slides) (Long division examples) (Case IV example)

Lecture 9, Sept 24: Improper Integrals (7.8) (slides) (examples)

Lecture 10, Sept 26: Applications of Integration: Arc length (8.1) (slides) (examples)

Lecture 11, Sept 28: Applications in Economics and Biology (8.4) (slides) (examples)

Lecture 12, Oct 1: Applications of integration in probability (8.5) (slides) (examples)

Lecture 13, Oct 3: Probability density functions (8.5) (slides) (examples)

Lecture 14, Oct 5: Average values (8.5) (slides) (examples)

Lecture 15, Oct 8: Differential Equations (9.1) (slides)

Lecture 16, Oct 10: Separable Differential Equations (9.3) (slides) (example)

Lecture 17, Oct 12: Separable Equations (9.3) (examples)

Lecture 18, Oct 15: Linear Differential Equations (9.5) (slides) (examples)

Lecture 19, Oct 17: Euler's Method (9.2) (slides)

Lecture 20, Oct 19: Euler's Method (9.2) and Predator-Prey Models (9.6) (slides) (example)

Lecture 21, Oct 22: Parametric Equations (10.1, 10.2) (slides)

Lecture 22, Oct 24: Examples of Parametric Equations and Parametric Calculus (10.1,10.2) (examples)

Lecture 23, Oct 26: Parametric Calculus Examples(10.2) (examples)

Lecture 24, Oct 29: Polar Coordinates and Calculus (10.3, 10.4) (slides) (examples)

Lecture 25, Oct 31: Polar Coordinates and Calculus (cont'd)

Lecture 26, Nov 2: Sequences (11.1) (slides)

Lecture 27, Nov 5: Sequences continued (11.1)

Lecture 28, Nov 7: Series (11.2) (slides) (induction example)

Lecture 29, Nov 9: Series cont'd (11.2)

Lecture 30, Nov 12: Series Comparison Tests (11.3-11.6) (slides)

Lecture 31, Nov 14: Series Comparison Tests continued (11.3-11.6)

Lecture 32, Nov 16: Absolute Convergence, Alternating Series, Ratio, Root, and Integral Tests (11.3-11.6)

Collection of worked examples for Sequences and Series (slides)

Lecture 33, Nov 19: Power series (11.8) (slides) (examples)

Lecture 34, Nov 21: Midterm III review session.

November 23: No class (Thanksgiving)

Lecture 35, Nov 26: Power series and Taylor Series (11.8-11.10) (slides) (examples)

Lecture 36, Nov 28: Taylor and Maclaurin Series (continued) (11.10)

Lecture 37, Nov 30: Taylor and Maclaurin Series (conclusion) (11.10) (examples)

Lecture 38, Dec 3: 3-Dimensional Coordinate Systems (12.1) (slides)

Lecture 39, Dec 5: Vectors (12.2) (slides)

Lecture 40, Dec 7: Vectors and the Dot Product (12.2, 12.3) (slides)

Lecture 41, Dec 10: Dot and Cross Products, Eqns of Lines and Planes (12.3-12.5)

Lecture 42, Dec 12: Review (Equation of plane example)