Description
This course covers optimization, multiple integrals, linear algebra, ordinary differential equations and partial differential equations.
Textbook: Math 2177, Custom Edition for OSU, Pearson, ISBN-13 9780137203833 or ISBN-10 0137203837. This custom textbook contains sections from the following textbooks:
Calculus for Scientists and Engineers: Early Transcendentals, by Briggs, Cochran, Gillett and Shulz, Chapters 13-15
Introduction to Linear Algebra, by Johnson, Riess, and Arnold, 5th edition
Fundamentals of Differential Equations and Boundary Value Problems, by Nagle, Saff and Snider, 8th Edition
Content
Math 2177 covers the following topics (in order):
| Section | Topic |
|---|---|
| 1.8 | Maximum/Minimum Problems |
| 1.9 | Lagrange Multipliers |
| 2.1 | Double Integrals over Rectangular Regions |
| 2.2 | Double Integrals over General Regions |
| 2.3 | Double Integrals in Polar Coordinates |
| 2.4 | Triple Integrals |
| 2.5 | Triple Integrals in Cylindrical and Spherical Coordinates |
| 2.7 | Change of Variables in Multiple Integrals |
| 3.1 | Vector Fields |
| 3.2 | Line Integrals |
| 3.3 | Conservative Vector Field |
| 4.1 | Introduction to Matrices and Systems of Linear Equations |
| 4.2 | Echelon Form and Gauss-Jordan Elimination |
| 4.2 | Echelon Form and Gauss-Jordan Elimination |
| 4.3 | Consistent Systems of Linear Equations |
| 4.5 | Matrix Operations |
| 4.6 | Algebraic Properties of Matrix operations |
| 4.7 | Linear Independence and Nonsingular Matrices |
| 4.7 | Linear Independence and Nonsingular Matrices |
| 4.8 | Data Fitting, Numerical Integration and Numerical Differentiation |
| 5.1 | Basic Ideas |
| Appx C | Complex Numbers |
| 5.2 | Linear Homogeneous Equations |
| 5.2 | Linear Homogeneous Equations |
| 5.3 | Linear Nonhomogeneous Equations |
| 5.3 | Linear Nonhomogeneous Equations |
| 5.4 | Applications |
| 6.1 | Introduction: A Model for Heat Flow |
| 6.2 | Method of Separation of Variables |
| 6.3 | Fourier Series |
| 6.3 | Fourier Series |
| 6.4 | Fourier Cosine and Sine Series |
| 6.5 | The Heat Equation |
| 6.6 | The Wave Equation |
Resources:
🚧 In the future, I will add a link to my lecture notes here.