Syllabus for Thomas Colthurst's 18.01/18.02 Section

• Instructor: Thomas Colthurst, thomasc@mit.edu. You can call me at 776-7634 any time before midnight.

• TA: Alicia Hardy, jillian@mit.edu.

• Text: George F. Simmons, Calculus with Analytic Geometry. (Either the first or second edition is fine.) In addition, you are encouraged to use the World Web Math hypertext book at http://web.mit.edu/wwmath/ to supplement your knowledge.

• Meeting Times: Mondays, Wednesday, and Fridays either at 9 am or 12 noon. You also have a one hour section on Tuesday at 1 pm or 7:30 pm with Alicia.

• Eligibility: To take 18.01/18.02, you should have already seen much of calculus. No knowledge of vector calculus is assumed.

• Credit: You will get 12 units of 18.01 credit and 12 units of 18.02 credit for completing this class. The 18.01 credit must count towards this (fall) semester; you can choose where to put the other 12 units -- either towards this semester, towards IAP, or towards the spring.

• Schedule: We will spend six weeks going over 18.01 material. There will be one test (on derivatives) and one final (on everything) during this time. We will then go on to cover 18.02. WE WILL NOT COMPLETE 18.02 BY THE END OF THE SEMESTER. Rather, you have the option of finishing 18.02 with Dana Pascovici during IAP period, or finishing it with me during the first six weeks of the spring semester.

• 18.03: Either way you decide to finish 18.02, you will still be able to sign up and be prepared for 18.03 in the spring.

• Assignments: There are homework assignments due every time we meet. These will consist of approximately five simple problems based on the reading. THEY ARE DUE THE SAME DAY AS THE READING. There will also be a more substantial weekly problem set due on our Tuesday meeting that will be based on the material covered the previous week. LATE HOMEWORK WILL NOT BE ACCEPTED except by special permission of the instructor.

• Grades: The grade in 18.01 will be based on the first test (30%), the final (40%), and homework (30%). The grade in 18.02 will be based on three hour long tests (15% each), a final (25%), and homework (30%).

Schedule of Classes

• Friday: Review of Pre-Calculus. Organizational Stuff.
  Assignment: Read Chapter 1 of Simmons.

• Tuesday: Limits. Domain of definition. Continuous Functions.
  Assignment (1st Edition): Read section 2.5, and Appendices C.1, C.2, and C.3. Do Problems 2.5, #3,5,7,17,19.
  Assignment (2nd Edition): Read sections 2.5 and 2.6, and appendices A.1, A.2, and A.3. Do Problems 2.5, #3,5,7,17 and 2.6, #1.

• Wednesday September 11: Derivatives. Motivation. Definition.
  Assignment (1st Edition): Read sections 2.1, 2.2, 2.3, and 2.4. Do Problems 2.3, #1,4, 6,11, and page 60, #7.
  Assignment (2nd Edition): Read sections 2.1, 2.2, 2.3, and 2.4. Do Problem s 2.3, #1,26,28,36, and page 81, #7.

• Friday September 13: Product and Quotient Rules. Derivatives of Polynomials.
  Assignment (1st Edition): Read sections 3.1 and 3.2. Do Problems 3.1, #1, and 3.2, #2, 8.
  Assignment (2nd Edition): Read sections 3.1 and 3.2. Do Problems 3.1, #1, and 3.2, #9 - 16, 46.

• Monday September 16: Chain Rule. Implicit Differentiation. Derivatives of Higher Order.
  Assignment (1st Edition): Read sections 3.3, 3.4, and 3.5. Do Problems 3.3 #1,5; 3.4 #1; 3.5, #2.
  Assignment (2nd Edition): Read sections 3.3, 3.5, 3.6. Do Problems 3.3 #17 - 22, 45; 3.5, #1-7; 3.6, #2.

• Tuesday September 17: (1st Edition): Page 60, #13; Page 84, #4, 22, 26, 42.
  (2nd Edition): Page 81, #13; Page 111, #4, 22, 26, 50.

• Wednesday September 18: Derivatives of Trigonometric Functions.
  Assignment (1st Edition): Read sections 9.1, 9.2, 9.4, 9.5. Do Problems 9.2, #1,2,5; 9.4, #1,2,6; 9.5, #4,5.
  Assignment (2nd Edition): Read sections 1.7, 2.5, 3.4, 9.1, 9.2, 9.4, 9.5. Do Problems 9.2, #1,2,5; 9.4, #1,2,6; 9.5, #4,5.

• Friday September 20: Derivatives of Logs and Exponents.
  Assignment: Read 8.1, 8.2, 8.3, 8.4, 9.7.
  (1st Edition): Do Problems 8.2, #1,2; 8.3, #1,3,5; 8.4, #2.
  (2nd Edition): Do Problems 8.2, #1,2; 8.3, #1,3,5; 8.4, #2.

• Monday September 23: Holiday.

• Tuesday September 24: (1st Edition) Page 223, #18, 21a; page 252, #26, 32; page 272, #19.
  (2nd Edition) Page 277, #18, 21a; page 305, #26, 32; page 330, #19.

• Wednesday September 25: Applications of Derivatives: Max-Min.
  Assignment: Read 4.1, 4.2, 4.3. Do problems 4.1, #3,5,15; 4.2, #1,11; 4.3, #3.

• Friday September 27: Applications of Derivatives II: Related Rates, Newton's Method, L'Hopital's Rule, Physics.
  Assignment: Read 4.5, 4.6, 12.1, 12.2, and 12.3.
  (1st Edition): Do Problems 4.5, #14; 4.6, #3, 8; 12.2, #1,2; 12.3, #1, 23.
  (2nd Edition): Do Problems 4.5, #14; 4.6, #3 (to two decimal places), 8; 12.2, #1,2; 12.3, #1,23.

• Monday September 30: First hour test.

• Tuesday October 1: (1st Edition) 4.1, #18, 4.3, #30; 4.5, #18; 12.2, #29; 12.3, #41, 42.
  (2nd Edition): 4.1, #18; 4.3, #30; 4.5, #18; 12.2, #29; 12.3, #41, 42.

• Wednesday October 2: Integration. Areas under graphs. Definition. Numerical Integration.
  Assignment: Read 6.1, 6.2, 6.3, 6.4, 6.5, 10.9.
  (1st Edition): Do Problems 6.5, #1; 10.9, #3.
  (2nd Edition): Do Problems 6.5, #1; 10.9, #3.

• Friday October 4: Fundamental Theorem of Calculus. Computing Integrals with the FTC.
  Assignment: Read 6.6, 6.7, 7.1, 7.2.
  (1st Edition): Do Problems 6.6, #1, 3a, 4a, 5a, 6, 7a; 6.7, #7, 13, 15.
  (2nd Edition): Do Problems 6.6, #1, 3, 6, 11, 22, 23, 6.7, #7, 13, 15.

• Monday October 7: Methods of Integration: Substitution, Integration by Parts, Tables.
  Assignment: Read 10.1, 10.2, 10.7, 10.8.
  (1st Edition): Do Problems 10.2, #1, 45, 49; 10.7, #1, 5.
  (2nd Edition): Do Problems 10.2, #1, 45, 49; 10.7, #1, 5.

• Tuesday October 8: (1st Edition): 6.3, #6; 6.5, #5; 10.9, #9; 6.7, #16; 7.2, #18.
  (2nd Edition): 6.3, #6; 6.5, #5; 10.9, #11; 6.7, #16; 7.2, #28.

• Wednesday October 9: Methods of Integration II: Partial Fractions, Completing the Square, Trig Substitution.
  Assignment: Read 10.3, 10.4, 10.5, 10.6.
  (1st Edition): Do Problems 10.3, #5, 19, 26; 10.4, #1, 3, 29; 10.5, #1,3; 10.6, #2, 6, 14.
  (2nd Edition): Do Problems 10.3, #5, 19, 26; 10.4, #1, 3, 29; 10.5, #1, 3; 10.6 #2, 6, 25.

• Friday October 11: Infinite Series. Sequences. Geometric Series. Some tests.
  Assignment (1st Edition): Read chapter 13, and sections 14.1, 14.2, 14.3, 14.4. Do Problems 14.2, #1, 3; 14.3, #1, 2, 3, 9; 14.4, #1.
  Assignment (2nd Edition): Read 13.1, 13.2, 13.3, 13.4, 13.5. Do Problems 13.2, #1, 3; 13.4, #1, 2, 3, 9; 13.5, #1.

• Monday October 14 and Tuesday October 15: No class (Columbus Day).

• Wednesday October 16: More tests: integral, ratio, root, alternating series.
  Assignment (1st Edition): Read 14.5, 14.6, 14.7. Do Problems 14.5, #1,3,9; 14.6, #1,5,16,18; 14.7, #1,3,27.
  Assignment (2nd Edition): Read 13.6, 13.7, 13.8. Do Problems 13.6, #1,3,9; 13.7, #1,5,16,18; 13.8, #1,3,27.

• Friday October 18: Power series. Taylor series.
  Assignment (1st Edition): Read 14.8, 14.9, 14.10, 14.11. Do Problems 14.8, #1,24; 14.9, #1,3; 14.10, #4.
  Assignment (2nd Edition): Read 14.1, 14.2, 14.3, 14.4, 14.5, 14.7. Do Problems 14.2, #1,24; 14.3, #1,3; 14.4, #4.

• Monday October 21: Review for 18.01 Final

• Tuesday October 22 (Evening): 18.01 Final (3 hours).

• Wednesday October 23: Overview of Vector Calculus. Curves, Surfaces, Volumes, Vector Fields. Tangent vectors, tangent planes. Averages, the volume under a graph.
  

• Friday October 25: Three dimensional Euclidean Geometry. Axioms. Pythagorean theorem. Projections. Cartesian Coordinates.
  Assignment (Both Editions): Read 18.1. Do 18.4, #1.

• Monday October 28: Vectors. Vector Algebra.
  Assignment (Both Editions): Read 17.3, 18.1. Do 17.3, #1a, 2a, 4, 5a.

• Tuesday October 29 (Both Editions): Problem Set: 17.3, #9, #10, #11; 18.1, #19.

• Wednesday October 30: Dot Product. Projections.
  Assignment (Both Editions): Read 18.2. Do 18.2, #1, 3a, 7, 13, 20a.

• Friday November 1: Cross Product. Determinants.
  Assignment (Both Editions): Read 18.3. Do 18.3, #1, 2, 3, 7.

• Monday November 4: Lines. Curves. Planes. Surfaces. Normal vectors. Parametric and implicit descriptions.
  Assignment (Both Editions): Read 18.4. Do 18.4, #5, 8, 9, 13, 18.

• Tuesday November 5: Problem Set (Both Editions): 18.2, #6, 9, 11; 18.3 #6, 10; 18.4, #15.

• Wednesday November 6: Cylindrical and Spherical Coordinates.
  Assignment (Both Editions): Read 18.7. Do 18.7, #1a, 2a, 3a, 4a, 5, 13.

• Friday November 8: Parametric Curves.
  Assignment: Read 17.1, 17.4. Do 17.1, #4; 17.4, #5, 8.

• Monday November 11: No class (Veterans Day).

• Tuesday November 12: Problem Set: 17.4, #11; handout problems.

• Wednesday November 13: Arc Length.
  Assigment: Read and do problems on handout.

• Friday November 15: Path integrals. Reparametrization.
  Assignment: Read and do problems on handout.

• Monday November 18: First hour test.

• Wednesday November 20: Functions of several variables. Graphing. Level curves (and surfaces). Slices.
  Assignment: Read 19.1, do 19.1, #14,16,24,25.

• Friday November 22: Domains of definition, limits, continuity.
  Assignment: Read 19.1 and handout. Do problems on handout and 19.1, #1,11,13.

• Monday November 25: Parital derivatives.
  Assignment: Read 19.2. Do 19.2, #2,3,4,9,21.

• Tuesday November 26: Problem Set: 19.2, #31; 19.3, #11,14,16.

• Wednesday November 27: Tangent planes.
  Assignment: Read 19.3. Do 19.3, #1,2,9,10.

• Friday November 29: No class (Thanksgiving).

• Monday December 2: Increments. Total differential. Fundamental lemma. Linear approximation.
  Assigment: Read 19.4 and handout. Do problems on handout.

• Wednesday December 4: Directional Derivatives. The gradient.
  Assignment: Read 19.5, do 19.5 #1a,2a,3a,4,5.

• Friday December 6: The Chain Rule.
  Assignment: Read 19.6, do 19.6 #1,5,7,8.

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  Revised Assignments

• Monday December 1: Cross Partials. Multidimensional Taylor series.

• Tuesday December 2: Problem Set: 19.5, #10; 19.6, #18.

• Wednesday December 4: Max-min.
  Assignment: Read. 19.7. Do 19.7, #1, 8, 10, 14.

• Friday December 6: Constrained Max-min. Lagrange Multipliers.
  Assignment: Read 19.8. Do 19.8, #1, #4, 5, 19.

• Monday December 9: Vector fields. Graphing. Flow lines.
  Assignment: Read handout.

• Tuesday December 10: Review for second hour test.

• Wednesday December 11: Divergence and curl.
  Assignment: Read handout.

• During Finals Period: Second hour test.

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  Over IAP/Spring Semester

• Line (work) integrals. Fundamental theorem of calculus for line integrals.
  Assignment: Read 21.1 and handout.

• Double integrals. Definition by Riemann sums. Cavaleri's principle. Iterated integrals.
  Assignment: Read 20.1, 20.2.

• Double integrals over general regions. Changing the order of integration.
  Assignment: Read 20.2.

• Triple integrals.
  Assignment: Read 20.5.

• Change of variables. Integration in polar, cylindrical, and spherical coordinates.
  Assignment: Read 20.4, 20.6, 20.7, 20.9.

• Applications of double and triple integrals.
  Assignment: Read 20.3.

• Third hour test.

• Parameterized surfaces. Normal vectors.
  Assignment: Read and do problems from handout.

• Surface area and surface integrals.
  Assignment: Read 20.8, A.22.

• Flux integrals.
  Assignment: Read and do problems from handout.

• Gauss' Theorem.
  Assignment: Read A.22.

• Stokes' and Green's Theorem.
  Assignment: Read 21.3, A.23.

• Further applications of Gauss', Stokes', and Green's theorems. Review of course. Preparation for final.