| Date | Topics | Text reference |
| Feb 5 | Introduction to R2 and R3. Points vs. vectors. Examples of curves and surfaces defined by algebraic equations. | 1.1 and 1.3 |
| Feb 7 | Vector-valued functions - parametrized curves in R2 and R3. Equation(s) of a line. Velocity and acceleration vectors. Arclength. | 1.2 and 1.4 |
| Feb 9 | Dot product in R2, R3, and Rn. Scalar and vector projections. Equation of a plane in R3. | 1.6 and 1.7 |
| Feb 12 | The cross product in R3. Intersection of lines and planes. Introduction to row reduction techniques. | 1.7, 1.8, and handout |
| Feb 14 | Unit tangent T and unit normal vector N for a parametrized curve. Tangential and normal components of acceleration. Curvature. Equations of motion. | 1.5, 4.3, and handout |
| Feb 16 | Introduction to functions of several variables with emphasis of functions of two and three variables. Graph of a function of two variables. Level curves (contours of a function of two variables. Level surfaces of a function of three variables. | 2.1 |
| Feb 21 | Vector fields in R2 and R3. Examples from physics and differential equations. | 5.1 and handout |
| Feb 23 | Integration of a function along a parametrized curve. Line integrals and work done by a variable force along a parametrized curve. | 5.1 and handout |
| Feb 26 | Partial derivatives. Continuity and differentiability of functions of several variables. Linear approximation and tangent planes. | 2.2, 2.3, and 2.5 |
| Feb 28 | Rate of change of a function along a parametrized curve. Basic chain rule. Directional derivative and the gradient vector. | 2.4 and 2.5 |
| Mar 2 | The gradient vector field of a function of several variables. Conservative vector fields, independence of path, and the Fundamental Theorem of Line Integrals. | 2.4 and 5.2 |
| Mar 5 | Higher order derivatives & quadratic approx. | 2.6 |
| Mar 7 | Review for Midterm Exam I | - |
| Mar 7 | Midterm Exam I - Wed, Mar 7, 4:00-5:30pm, Sci Ctr Hall C | - |
| Mar 9 | Application: Partial differential equations in physics | Supplement |
| Mar 12 | Extrema of functions of several variables. Unconstrained optimization. | 2.7 and handout |
| Mar 14 | Constrained optimization and the method of Lagrange multipliers. | 4.4 and handout |
| Mar 16 | Applications in economics | Supplement |
| Mar 19 | General chain rule. Implicit differentiation. Economics applications. | 2.8 and handout |
| Mar 21 | Integration over regions in R2 and R3. Average value of a function. | 3.1 |
| Mar 23 | Iterated integrals and the Fubini Theorem. | 3.2 |
| Apr 2 | Integrals in polar coordinates (R2) and cylindrical coordinates (R3). | 3.3 and 3.4 |
| Apr 4 | Integrals in cylindrical and spherical coordinates. | 3.4 |
| Apr 6 | Applications: centroids, center of mass, moment of inertia. | Handout |
| Apr 9 | Change of variables in multiple integrals. Jacobian matrices. | 3.5 |
| Apr 11 | Review for Midterm Exam II. | - |
| Apr 11 | Midterm Exam II - Wed, Apr 11, 4:00-5:30pm, Sci Ctr Hall C | - |
| Apr 13 | Line integrals and Green's theorem. | 5.3 |
| Apr 16 | Parametrized surfaces in R3. | 5.4 |
| Apr 18 | Surface integrals, surface area. | 5.5 and handout |
| Apr 20 | Flux of a vector field through a surface. | 5.6 |
| Apr 23 | Divergence of a vector field and the Divergence Theorem. | 5.6, 5.7, and handout |
| Apr 25 | Curl of a vector field and Stokes' Theorem. | 5.6, 5.7 and handout |
| Apr 27 | Review of Five Fundamental Theorems of Calculus. | 5.7 and handout |
| Apr 30 | Applications to differential equations: The Heat Equation. | Supplement |
| May 2 | Applications in physics: Maxwell's Equations. | Supplement |
| May 4 | Last details | - |
There will be several homework assignments during the semester which will require the use
of mathematical software such as Mathematica, Maple, or Matlab in order to do a
satisfactory job.