Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. Vector algebra in 3D, vector- valued functions, gradient, divergence and curl, Taylor series, numerical methods and applications. Given in the first half of the first term. However, those wishing credit for 18.013A only, must attend the entire semester. Prerequisites: a year of high school calculus or the equivalent, with a score of 4 or 5 on the AB, or the AB portion of the BC, Calculus test, or an equivalent score on a standard international exam, or a passing grade on the first half of the 18.01 Advanced Standing exam.

Spreadsheets Across the Curriculum activity. In advance of an actual lab activity, students virtually simulate the calibration of a laboratory micropipettor. QL: Accuracy and precision.

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

Spreadsheets Across the Curriculum module. Students build a spreadsheet to find the combination of mini-pizzas and calzones that maximizes revenue given constraints on labor time and baking time.

This activity is about planetary climate. Once familiar with the factors that determine a planet's surface temperature, learners will use an interactive spreadsheet model of a planet's atmosphere to determine if greenhouse gases, luminosity of the source, the distance of the planet from the source and the albedo of the planet can be manipulated so that the average surface temperature on Mars or Venus could support human life. Learners will then be asked to make some conclusions about these methods and suggest improvements for the spreadsheet model (see related resources for link to this model). The activity requires use of Microsoft Excel software. This is Activity D in the fourth module, titled "How do Atmospheres Affect Planetary Temperatures?," of "Earth Climate Course: What Determines a Planet's Climate?."

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

This is an activity about classifying planetary characteristics. Learners will analyze the provided information about each planet in order to make graphs and Venn diagrams. Then, using both, learners will identify similarities and differences of the planets in the Solar System. This is Activity C-11 as part of The Universe At Your Fingertips curriculum, available for purchase.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.

Measurement and common math are required to perform your job duties in nearly every aspect of conveyor manufacturing. I have compiled a list of skills relating to math and measurement that are essential for successful job performance. This include being able to:

Read a tape measure accurately
Add or subtract fractions
Convert fractions to decimal form
Use a decimal equivalent card or chart (drill gage)

In this task, students can see that if the price level increases and peopleŐs incomes do not increase, they arenŐt able to purchase as many goods and services; in other words, their purchasing power decreases.

Using the story "The Celebrated Jumping Frog of Calaveras County" by Mark Twain, learners simulate a jumping-frog contest and determine the distances "jumped." Learners record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). Learners compare the range and median of the total distances with those of the official distances of the group.

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).