Last Updated: December 15, 2015
Math 2070 Mathematical Methods in Engineering
Section 1
220 Turead
9:30 - 10:20 MTWTh
Solutions to Final Exam Posted
| Class | Date | Topic | Section | Suggested Problems |
|---|---|---|---|---|
| 1 | Aug 24 | Matrix Operations | 8.1 | 1 - 21 (Odd) |
| 2 | Aug 25 | Linear Equations-1 | 8.2 | 1 - 25 (Odd) |
| 3 | Aug 26 | Linear Equations-2 | ||
| 4 | Aug 27 | Invertible Matrices | 8.3 | 1 - 15 (Odd) |
| 5 | Aug 31 | Determinants | 8.4 | 1 - 15 (Odd) |
| 6 | Sept 1 | Intro to Diff Equations/Direction Fields | 1.1, 1.2 | 1.1: 1, 5, 7, 11, 13, 17, 19, 25, 27, 33; 1.2: 5-13 (Odd) |
| 7 | Sept 2 | Separable Differentiable Equations | 1.3 | 11, 14, 15, 17, 19, 25, 27, 34, 35 |
| 8 | Sept 3 | Linear First Order Equations | 1.4 | 1, 3, 5, 9, 13, 16, 17, 18, 21, 23, 25 |
| 9 | Sept 8 | First Order Models: Mixing and/or First Order Circuits | 1.4, Circuit Sup. | 1.4: 27, 29, 31; Circuits: 1, 3, 5 |
| 10 | Sept 9 | Laplace Transform Method | 2.1 | 1 - 13 (Odd) |
| 11 | Sept 10 | Basic Laplace Transform Formulas | 2.2 | 1 - 35 (Odd) |
| 12 | Sept 14 | Review for Exam 1 | ||
| 13 | Sept 15 | Exam 1 | ||
| 14 | Sept 16 | Partial Fractions I | 2.3 | 13, 15, 19, 23, 25, 27, 31, 33, 35, 37 |
| 15 | Sept 17 | Partial Fractions II | 2.4 | 7, 9, 11, 13, 17, 19 |
| 16 | Sept 21 | Laplace Inversion | 2.5 | 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 35, 36 |
| 17 | Sept 22 | The spaces Eq : Special Cases | 2.6 | 1 - 25 (Odd) |
| 18 | Sept 23 | The spaces Eq : General Case | 2.7 | 1 - 27 (Odd) |
| 19 | Sept 24 | Convolution | 2.8 | 1 - 27 (Odd) |
| 20 | Sept 28 | Basic Constant Coefficient Linear DE | 3.1, 4.1 | 3.1: 1 - 19 (Odd); 4.1: 1 - 11 (Odd) |
| 21 | Sept 29 | Linear Independence | 3.2 | 1 - 25 (Odd) |
| 22 | Sept 30 | Linear Homogeneous DE | 3.3, 4.2 | 3.3: 1-15 (Odd); 4.2: 1 - 11 (Odd) |
| 23 | Oct 1 | Undetermined Coefficients | 3.4, 4.3 | 3.4: 1-27 (Odd); 4.3: 1 - 7 (Odd) |
| 24 | Oct 5 | Spring Systems I | 3.6 | 1 - 15 (Odd) |
| 25 | Oct 6 | Spring Systems II/ RCL Circuits | 3.7 | 1 - 4 |
| 26 | Oct 7 | Review | ||
| 27 | Oct 8 | Exam 2 | ||
| 28 | Oct 12 | Existence/Uniqueness for Second Order Linear DE | 5.1 | 1 - 23 (Odd) |
| 29 | Oct 13 | Homogeneous Equations | 5.2 | 1 - 9 (Odd) |
| 30 | Oct 14 | Cauchy-Euler Equations | 5.3 | 1 - 15 (Odd) |
| 31 | Oct 15 | Reduction of Order | 5.5 | 1 - 11 (Odd) |
| 32 | Oct 19 | Variation of Parameters | 5.6 | 7 - 15 (Odd) |
| 33 | Oct 20 | Discontinuous Functions | 6.1 | 1 - 8 |
| 34 | Oct 21 | Heaviside Class | 6.2 | 9-23 (Odd), 29-41 (Odd) |
| 35 | Oct 22 | Laplace Transform Method II | 6.3 | 1 - 11 (Odd) |
| 36 | Oct 26 | Dirac Delta Function | 6.4 | 1 - 9 (Odd), 15, 17 |
| 37 | Oct 27 | |||
| 38 | Oct 28 | Linear Systems of DE | 9.1, 9.2 | 7, 9, 11, 13, 17, 19, 27, 29, 31, 33, 35 |
| 39 | Nov 2 | Review | ||
| 40 | Nov 3 | Exam 3 | ||
| 41 | Nov 4 | Matrix Exponential and Laplace Transform | 9.3 | 1, 3, 9, 11, 13, 15 |
| 42 | Nov 5 | Fulmer's Method | 9.4 | 1 - 19 (Odd) |
| 43 | Nov 9 | 9.4 | ||
| 44 | Nov 10 | Constant Coefficient Linear Systems | 9.5 | 1 - 15 (Odd) |
| 45 | Nov 11 | Periodic Functions | 10.1 | 1 -23 (Odd), 28 |
| 46 | Nov 12 | Fourier Series | 10.2 | 1 - 15 (Odd) |
| 47 | Nov 16 | Convergence of Fourier Series | 10.3 | 1 - 13 (Odd) |
| 48 | Nov 17 | Fourier Sine and Cosine Series | 10.4 | 1 - 11 (Odd) |
| 49 | Nov 18 | Operations on Fourier Series | 10.5 | 1 - 5 |
| 50 | Nov 19 | Applications of Fourier Series | 10.6 | 1 - 9 (Odd) |
| 51 | Nov 23 | Review | ||
| 52 | Nov 24 | Exam 4 | ||
| 53 | Nov 25 | Separation of Variables for PDE | ||
| 54 | Nov 30 | One Dimensional Heat Equation | ||
| 55 | Dec 1 | Laplace Equation | ||
| 56 | Dec 2 | Review | ||
| 57 | Dec 3 | Review |
Homework to be Collected
| Homework | Date Due | Solutions |
|---|---|---|
| Homework # 1 | Aug 31 | Solutions |
| Homework # 2 | Sept 8 | Solutions |
| Homework # 3 | Sept 14 | Solutions |
| Homework # 4 | Sept 23 | Solutions |
| Homework # 5 | Sept 28 | Solutions |
| Homework # 6 | Oct 6 | Solutions |
| Homework # 7 | Oct 21 | Solutions |
| Homework # 8 | Oct 28 | Solutions |
| Homework # 9 | Nov 16 | Solutions |
| Homework # 10 | Nov 23 | Solutions |
| Homework # 11 | Dec 3 | Solutions |
Exam 1 Review Answers
Exam 2 Review
With Answers
Exam 3 Review (with answers)
Exam 4 Review (with answers)
Final Exam Review (with answers)
The following are Math 2070 exams given in recent semesters. Solutions are provided, if available.
| Fall 2013 | Spring 2014 | Fall 2014 | Spring 2015 | ||||
| Exam 1 | Solutions | Exam 1 | Solutions | Exam 1 | Solutions | Exam 1 | Solutions |
| Exam 2 | Solutions | Exam 2 | Solutions | Exam 2 | Solutions | Exam 2 | Solutions |
| Exam 3 | Solutions | Exam 3 | Solutions | Exam 3 | Solutions | Exam 3 | Solutions |
| Exam 4 | Solutions | Exam 4 | Solutions | Exam 4 | Solutions | Exam 4 | Solutions |
| Final Exam | Solutions | Final Exam | Solutions | Final Exam | Solutions | Final Exam | Solutions |
Some additional exams from earlier years. The coverage and notation may be slightly different.
Fall 1994 Exam 5 Solutions
Fall 1994 Final Exam Solutions
Spring 1996 Exam 5 Solutions
Exam Schedule
| Exam | Date | Solutions |
|---|---|---|
| Exam 1 | September 15 | Solutions |
| Exam 2 | October 8 | Solutions |
| Exam 3 | November 5 | Solutions |
| Exam 4 | November 24 | Solutions |
| Final Exam | Dec 11(Friday) 7:30 - 9:30 AM | Solutions |