NOTE: Carlos
will have office hours on Tuesday, December 9 from 4-5:30 PM in Amos Eaton
429.
His students can pick up exam #3 at that time.
** FINAL EXAM INFORMATION **
Our final exam is on Thursday, December 11 from 6:30 - 9:30 PM in Sage 3303
No calculators are permitted in the exam.
All of the formulas that were supplied during the first three exams will be included on the final exam.
The final exam will consist of two parts:
Part 1 will contain 3 problems, all of which you must do, worth 15 points
(45 points)
Part 2 will contain 4 problems, worth 20 points each. You must do 3 of
the 4 (60 points)
You must indicate on the exam which one of the Part 2 problems you do not
want graded.
Thus, the final is worth 105 points just like the other exams.
There will be a review class for the final on Wednesday,
December 10 from 3 - 5 PM in Sage 3303.
Here are some practice
problems to work on.
Prof. Schmidt will also have office hours on Thursday, December 11 from 11 AM - 12:30 PM
The exam will cover the following topics:
Classification of Diff Eqs (Linearity,
Order, etc.) (Section 1.3)
Solving 1st Order Linear ODEs: Method
of Integrating Factor (Section 2.1)
Existence and Uniqueness of Solutions
to 1st Order Linear ODEs (Section 2.4)
Separation of Variables (Section 2.2)
Differences Between Linear and Non-Linear
1st Order ODEs (Section 2.4)
Modeling Problems With Linear 1st
Order ODEs (Section 2.3)
Autonomous Equations and Population
Models (Section 2.5)
Constant-Coefficient 2nd Order Homogeneous
ODEs: Method of Characteristic Roots (Section 3.1)
Theory of 2nd Order Linear ODEs, Wronskian
Determinant (Section 3.2)
Linear Independence and Abel's Theorem
(Section 3.3)
Complex Characteristic Roots and Euler's
Formula (Section 3.4)
Repeated Characteristic Roots (Section
3.5)
Reduction of Order (Section 3.5)
Abel's Formula and Finding a 2nd Independent
Solution (3.5)
Non-Homogeneous Equations and
Method of Undetermined Coefficients (3.6)
Spring-Mass Systems (3.8)
Two-Point Boundary Value Problems
(10.1)
The Heat Conduction Problem
(10.5)
Fourier Series, Euler-Fourier
Formulas (10.2)
The Fourier Theorem (10.3)
Odd and Even Functions,
Sine and Cosine Series (10.4)
Solving the Heat Conduction
Problem (10.5)
Systems of 1st order ODEs
(7.1)
Basic Matrix Algebra (Computing
Inverse Matrices NOT included) (7.2)
Solving systems of the
form Ax = 0 using gaussian elimination (7.3)
Linear Independence of
Vectors (7.3)
Eigenvalues and Eigenvectors
of a square matrix A and how to find them (7.3)
The Wronskian and Fundamental
Sets of Solutions (7.4)
Solving Constant Coefficient
Systems of ODEs (7.5)
Classification of the
Origin by type and stability (7.5, 9.1)
Sketching Phase Portraits
(7.5,9.1)
Complex Eigenvalues (7.6)
The trace-determinant
plane (9.1 exercise and notes)
Office Hours Information (valid through Friday, December 5):
Dave Schmidt's Office Hours (in Amos Eaton 408): Wednesday 3 - 5 PM, Thursday 11AM - 12PM
Recitation Instructor Office Hours: Carlos Lopez
Rajesh Nimbalkar
Homework Resources:
Exam Resources:
MAPLE Resources: