Intermediate Calculus II

This course is designed to round out the typical Calc I-III courses completing all topics brushed upon in these courses and providing a mastery of the techniques of calculus. It will include introductory ordinary differential equations, centers of mass and moments of inertia with applications to probability, advanced integration techniques, series in several variables, plane curves and their curvature, Triple Integrals and Jacobians, Parametric surfaces, Divergence and Stokes Theorem, and an introduction partial differential equations. Applications will be stressed throughout.

Grading: 60% of the class grade will be based on projects (worth 5 pts each for the best 12) and 40% on the 4 exams including the final (10% for each).

15 Projects: A large part of this course will be projects which will be done in groups in class. Each group will submit one copy of each project signed by every member of the group. The teams will be switched around as the course progresses. The projects will be due at the end of class. Students who miss class will get a 0 on the project but the bottom three grades on projects will be dropped.

3 Exams and Final: There will be three in class exams before spring break which will test material similar to the homeworks and projects. The final exam will only cover work from after the Spring break. Calculators will be permitted on all exams.

Syllabus:

• Tuesday Jan 28: Space Curves (11.1-3)
  Classwork: Project 1: finding the formula for a space curve.
  Homework: Read 11.1-3, do 11.3/41, 43, 45, 46,
• Thursday Jan 30: Arclength and Reparametrization (11.4-11.5),
  Classwork: Project 2: 11.5/13
  Homework: Read 11.4-5, Do 11.4/3, 19, 39, 11.5/13,14, Chap 11 Review/ 17, 19
• Tuesday Feb 4: Curvature (11.5)
  Classwork: Maple demo, Project 3: Chap 11 review: 58*, 59*, 60*
  Homework: 11.5/ 33, 41,42, Handout: Parametrization Invariants
• Thursday Feb 6: Maximization and Lagrange Multipliers
  Classwork: Project 4: Handout
  Homework: Complete the maximization handout and do the Homework practice for Exam I handout. These handouts are available on the door to my office (200B Gillet Hall). Take one of each if you missed class.
• Tuesday Feb 11: Review
  Classwork: Review
  Homework:
• Thursday Feb 13: Exam I
  Homework: review 5.2 Examples 1-6, solve for general solutions: (a)dy/dx=x/y, (b) dy/dx= (x^2+2)/(3y^2) , (c) 4yy'-3e^x=0. and solve for particular solutions: (d) yy'-e^x=0 y(0)=4, (e) y(x+1)+y'=0 where y(-2)=1. Solutions
• Tuesday Feb 18: Snow Day! Lehman is Closed!
  Homework: Read 14.1 This should be review of material you've learned in Vector Calculus. (a) If V= (-y, x), plot V at (0,0), (0,1), (1,1), (1,0), (-1, 0), (0,-1) (-1,1) (-1,-1) and (1, -1) then find div(V) and curl(V). (b) If V= (x,y) plot V at (0,0), (0,1), (1,1), (1,0), (-1, 0), (0,-1) (-1,1) (-1,-1) and (1, -1) then find div(V) and curl(V). Note: to take the curl of V assume is is a three vector with third component =0 and no dependence on z.
• Thursday Feb 20: Vector Fields and ODE's 14.1
  Classwork: Project 5: solving for a space curve c(t) such that c'(t)=V(c(t))
  Homework: Catch up on old homework, Redo Exam I at home, Finish Project V, Read 14.1-2,
• Tuesday Feb 25: Div, Curl, Line Integrals and Conservative Fields 14.2-3
  Classwork: 15 minutes to finish Project 5 at the end of class.
  Homework: 14.2-3
• Thursday Feb 27: Line Integrals and Potential Functions
  Classwork: Project 6: solving for f given its gradient
  Homework:
• Tuesday Mar 4: Green's Theorem (14.4)
  Classwork: Start Project 7.
  Homework:
• Thursday Mar 6: Curl V and the potential, 2D div thm (14.4)
  Classwork: Finish Project 7.
  Homework: Study then do all examples in section 14.4 and check your answers.
• Tuesday Mar 11: Guest Speaker on ODE,
  No office hours before class, extra hours on Thurs Mar 13 6-7:30 pm,
  Project 7 will be returned in class and a sample exam will be given.
  Homework: Review for the exam
• Thursday Mar 13: Exam II on ODE (Separation of Variables), Div, Curl, plotting vector fields, space curves, Line Integrals, examples from 14.4 and Projects 5-7.
  Classwork:
  Homework:
• Tuesday Mar 18: Integration with polar coordinates 13.3 (9.4-6)
  Classwork: Project 8: practice integrating (due Tuesday Mar 25)
  Homework: Review 10.7 and determinants
• Thursday Mar 20: Jacobians (13.7-13.8)
  Classwork:
  Homework: finish Project VIII plus assignment by Prof Fisher
• Tuesday Mar 25: Heat Equation, a partial differential equation
  Classwork: Project 9: The Heat Equation
  Homework: Project 9: 1-4, finish Jacobian assignment
• Thursday Mar 27: The heat equation continued
  Classwork: Project 9 continued
  Homework: Finish project 9
• Tuesday April 1: Parametric Surfaces (14.5), Surface Integration 14.6
  Classwork: Maple demonstration
  Homework: Read 14.5-6, do odd problems 14.5/1-12
• Thursday April 3: Flux Integrals and Divergence Theorem (14.6-14.7)
  Classwork: Project 10: do last page of project 7, 14.6/23,25 14.7/9, 11 draw pictures to go with your problems or print with a Maple program
  Homework: finish Project 10
  Study for Exam III: Study all the topics and projects since Exam II, practice applying Green's Theorem as in Project 8, redo the homework on Jacobians from 13.7-8, redo problem 1 from project 9, redo homework from 14.5, redo problems from 14.6 and 14.7, be sure to understand how to apply the Divergence Theorem. The exam will not consist of complete long problems but instead will be multiple choice style in which you choose from 4 answers (similar to the GRE). Part of the exam will be open book so bring your notes and textbook.
• Tuesday April 8: Hand in Project 10, Review for Exam III
  Classwork:
  Homework:
• Thursday April 10: Exam III
  Homework: Project 11 on Stoke's Theorem due April 29
  (read 14.8, do 14.8/7,9 and page 1090 problem 1)
• Tuesday April 15- Thursday April 24: No class
  Tuesday April 15 follows a Wednesday schedule
  Homework: Work on Project 11
• Tuesday April 29: Continuity 12.2 (f:R^n to R^m)
  Classwork: start Project 12: epsilons and deltas individually
  Homework:
• Thursday May 1: Continuity Continued
  Classwork: maple
  Homework: finish project 12, review Taylor series
• Tuesday May 6: Differentiability
  Classwork: project 13
  Homework: finish project 13
• Thursday May 8: Multivariable Taylor Series
  Classwork: project 14
  Homework: finish project 14
• Tuesday May 13: Applications
  Classwork: Project 15: using Taylor series to solve the heat equation
  Homework:
• Thursday May 15: Review (last class)
  Classwork: Watch Inside/Out video about how to turn a sphere inside out.
  Homework: Study practice exam and do project 15
  Answers to practice exam: (1) C (2) B (3) A (4) C (5) A (6) A (7) B (8) (-1,0,0) (9) A (10) B (11) D (12) C (13) A (14) A (15) B
  
• Tuesday May 20: Office Hours 4-8pm
• Thursday May 22: Final Exam 8-10 pm Room 205 Gillet Hall