MAT 303: Calculus IV with applications

Spring 2016

Syllabus



Instructor's Contact Details:
Instructor: Dr. Luigi Lombardi
E-mail: luigi.lombardi AT stonybrook.edu
Office: Math Tower 3-120
Office hours: Tuesday & Thursday 1pm-2pm in Math Tower 3-120
            Thursday 12pm-1pm in MLC
            By appointment

Lecture (location and time):
Location: Library W4550
Time: Monday-Wednesday-Friday 10am-10:53am

Teaching Assistant's Contact Details:
Teaching Assistant: Zeyu Cao
Office: MLC (Mathematical Learning Center) in Math Tower S-Level
Office Hours: Friday 10am-11am and Tuesday & Thursday 5:30pm-6:30pm in MLC
E-mail: zeyu.cao@stonybrook.edu

Recitation Sections:
R01: Friday 12pm - 12:53pm in Library E4310
R02: Wednesday 12pm - 12:53pm in Library W4540

Textbook:
C. H. Edwards, D. E. Penney, D. T. Calvis "Differential equations and boundary value problems", 5th edition, Pearson Prentice Hall

Course Description:
This is a course about differential equations. We will study first-order differential equations, numerical methods, linear equations of higher-order, homogeneous and non-homogeneous equations, linear systems of differential equations, stability. A particular eye is given to techniques of solutions of differential equations and to the description of models coming from physics, chemistry, and economics.

Prerequisites:
Completion of one of the standard calculus sequences (either MAT 125-127 or MAT 131-132 or MAT 141-142) with a grade C or higher in MAT 127, 132 or 142 or AMS 161. Also, MAT 203/205 (Calculus III) and AMS 261/MAT 211 (Linear Algebra) are recommended. Informally, students should know integration and differentiation techniques and, desirably, be familiar with complex numbers and basic aspects of linear algebra.

Midterms:

Practice Final Exam
Solutions to Practice Final Exam Part I (Problems 1-4)
Solutions to Practice Final Exam Part II (Problems 5-8)
Solutions to Practice Final Exam Part III (Problems 9-11)
Solutions to Practice Final Exam Part IV (Problem 12)

Summary Topics

Practice Midterm II
Solutions to Practice Midterm II

Practice Midterm I
Solutions to Practice Midterm I

Final Exam:
Final Exam on Monday May 16th, 2016 at 8am - 10.45am: in Library W4550.

Homework:
There will be weekly homework assignments to be turned in to your TA at the beginning of your next recitation section. You are encouraged to work in groups, or to consult each other, or me, or the teaching assistant, in order to solve the homework set. However the writing-up of your homework should reflect your own understanding. It is very important that you work out each homework assignment as they will help you to solve the problems of the midterms and the final exam. Late homework will not be graded.

Assignments:
  • Assignment 1: 1.1: 1, 4, 5, 32; 1.2: 2, 7, 11, 14, 25, 27, 37 (Due date: February 12th)
  • Assignment 2: 1.3: 12, 14, 28; 1.4: 1, 4, 6, 23, 25, 27, 35, 47 (Due date: February 15th)
  • Assignment 3: 1.5: 1, 3, 6, 17, 37; 1.6: 1, 2, 13, 20, 31, 34 (Due date: February 22nd)
  • Assignment 4: Solve all problems of the Practice Midterm I without the asterisks, and in addition 1 problem with an asterisk at your choice except for Problem 2. (Due date: February 29th)
  • Assignment 5: 2.1: 10, 13, 21; 2.2: 19 (Due date: March 9th/11th in Recitation Sections)
  • Assignment 6: 2.3: 2; 3.1: 1, 3, 22, 25, 33, 39, 31; 3.5: 1 (Due date: March 23rd/25th in Recitation Sections)
  • Assignment 7: 3.2: 7,8; 3.3: 11, 13, 18, 27, 31; 3.5: 1, 3, 4, 12 (Due date: March 30th/April 1st in Recitation Sections)
  • Assignment 8: (Due date: April 13th/15th in Recitation Sections)
  • Assignment 9: (Due date: April 20th/22th in Recitation Sections)
  • Assignment 10: (Due date: April 29th in Recitation Sections)
  • Assignment 11: (Due date: May 6th in Recitation Sections)
    Midterms and Final Exam:
    During the semester there will be two midterms to be taken in class during lecture hours. The final exams will occur in May. The dates of both the midterms and the final exam will be announced later on. Makeup exams will only be given in the event that circumstances beyond the students control do not allow the student to take the exams at the assigned times.

    Course Grading:
    20% Homework
    20% Midterm 1
    20% Midterm 2
    40% Final Exam

    Academic Integrity:
    Each student must pursue his or her goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Instructors are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, see the academic judiciary web site at http://www.stonybrook.edu/cinncms/academic-integrity/index.html

    Diary of Classes:
    4
    Week Material Covered Assignment Homework Additional Exercises Notes
    Week 1 (Jan. 25th-29th) 1.1: Differential Equations and Mathematical Models 1.1: 1, 4, 5, 32; 1.2: 2, 7, 11, 14, 25, 27, 37 (due on Feb. 12th) 1.1: 7, 9, 43; 1.2: 6, 10, 33, 35
    1.2: Integrals as General and Particular Solutions
    Week 2 (Feb. 1st-5th) 1.3: Slope fields and solutions curves 1.3: 12, 14, 28; 1.4: 1, 4, 6, 23, 25, 27, 35, 47 (due on Feb. 15th) 1.3: 16, 30; 1.4: 5, 10, 28, 33, 51
    1.4: Separable differential equations Notes on the exponential equation and mathematical models
    Week 3 (Feb. 8th-12th) 1.4: Exponential equation and Mathematical Models 1.5: 1, 3, 6, 17, 37; 1.6: 1, 2, 13, 20, 31, 34 (due on Feb. 22nd) 1.5: 14, 17, 36, 38; 1.6: 4, 16, 21, 59, 62
    1.5: Linear first order differential equations
    Week 4 (Feb. 15th-19th) 1.5: Mixture problems and 1.6: Substitution methods All problems of the Practice Midterm I without the asterisk, plus 1 problem at your choice with an asterisk except Problem 2 (due date Feb. 29th) 1.2: 35, 36; 1.3: 30; 1.4: 41, 51, 52; 1.5: 22, 23, 24, 38; 1.6: 15, 21, 36, 59
    1.6: Substitution Methods - Homogeneous equations, Bernoulli equations
    1.6: Exact Differential Equations Examples of exact differential equations
    Week 5 (Feb. 22th-26th) 2.1: Population Models: Logistic Equation 2.1: 10, 13, 21; 2.2: 19 (due on March 9th/11th in Recitation Sections) 2.1: 2, 18, 30; 2.2: 23
    2.1: Logistic Equation and 2.2: Equilibrium solutions and stability
    2.2: Bifurcation
    Week 6 (Feb. 29th-March 4th) Review Midterm I
    Midterm I
    2.3: Acceleration-velocity models and 2.4: Euler Method
    Week 7 (March 7th-11th) 3.1: Introduction: Second-order linear equations 2.3: 2; 3.1: 1, 3, 22, 25, 33, 39, 31; 3.5: 1 2.3:4, 6; 3.1: 21, 23, 36, 38
    3.1: Introduction: Second-order linear equations
    3.5: Undetermined Coefficients Method for homogeneous second-order linear equations
    Week 8 (March 14th-18th) Spring Break
    Week 9 (March 21th-25th) 3.2: General solutions of linear equations 3.2: 7,8; 3.3: 11, 13, 18, 27, 31; 3.5: 1, 3, 4, 12 (due date March 30th / April 1st)
    3.3: Homogeneous Equations with constant coefficients
    Week 10 (March 28th - April 1st) 3.5: Nonhomogeneous Equations Practice Midterm II
    Review Midterm 2
    Week 11 (April 4th - April 8th) 3.4: Mechanical Vibrations and Review Midterm 2
    Midterm II (April 6th)
    4.1: First-order systems Assignment 8 (sections 3.4, 3.5, 4.1)
    Week 12 (April 11th - April 15th) 5.1: Matrices and linear systems
    5.2: The eigenvalue method (distinct real solutions) Assignment 9
    Week 13 (April 18th - April 22th) 5.2: The eigenvalue method (complex solutions)
    5.5: The eigenvalue method (multiple solutions)
    Week 14 (April 25th - April 29th) 5.5: The eigenvalue method (multiple solutions) Assignment 10 (due date April 29th)
    5.6: Exponential matrix
    5.7: Undetermined coefficients for linear systems
    4.2: Elimination method for systems of differential equations (homogeneous and non-homogeneous)
    Week 15 (May 2nd - May 6th) Review I Assignment 11 (due date May 6th)
    Review II
    Review III
    Final Exam on Monday May 16th at 8.00am