Multivariable Calculus by Ostebee and Zorn.
| Section 1.1 | 3-D space and surface. |
| Section 1.2 | Parametric curves. |
| Section 1.3 - 1.4 | Vectors, vector valued functions. |
| Section 1.5 | Derivatives, anti-derivatives and motion. |
| Sections 1.6 - 1.7 | Dot product, lines and planes |
| Sections 1.7 - 1.8 | Lines, planes and cross product. |
| Appendix C | Introduction to matrices. |
| Sections 2.1 & 1.1 | Functions of several variables. |
| Sections 2.2 - 2.3 | Partial derivatives, contours & linear approximations. |
| Sections 2.3 - 2.4 | Linear approximations and the gradient. |
| Sections 2.5 - 2.6 | Theory of derivatives, high order derivatives & quadratic approx. |
| Section 2.7 | Max-min, critical points and extreme points. |
| Sections 2.7 & 4.4 | More on extreme points, constrained optimization. |
| Section 4.4 | Constrained optimization. |
| Section 2.8 | Multivariable chain rule. |
| Section 3.1 | Multiple integrals. |
| Section 3.2 | Calculating integrals by iteration. |
| Section 3.3 | Integrals in polar coordinates. |
| Section 3.4 | Integrals in spherical and cylindrical coordinates. |
| Section 5.1 | Line integrals and vector fields. |
| Section 5.2 | The fundamental theorem of line integrals. |
| Section 5.3 | Line integrals and Green's theorem. |
| Section 5.4 | Surfaces and parameterizations. |
| Section 5.5 | Surface integrals |
| Section 5.6 | Derivatives of vector valued functions, div and curl. |
| Section 5.7 | Stokes' theorem. |
| Section 5.8 | Divergence theorem. |
| Sections 5.7 - 5.8 | More on Stokes' & Divergence Theorems. |
| Handouts | Differential equations. |
There will be approximately three homework assignments during the semester which will
require the use of mathematical software such as Mathematica, Maple, or Matlab.
Work & Energy, Angular Momentum, Planetary Motion, Relativity, Center of Mass, Electricity & Magnetism, Euler's Equation, Wave Equations, Heat Equation, Laplace's Equation, Schrodinger's Equation, Dirac's Equation.
Midterm Exam 1: Tuesday, February 29, 7:00pm to 8:30pm in Sci
Ctr Hall C
Midterm Exam 2: Tuesday, April 4, 7:00pm to 8:30pm in Sci Ctr
Hall C
Final Exam (tentative): May 25