This course is an introduction to differential and integral calculus. It begins …
This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and use it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions.
Published in 1991 and still in print from Wellesley-Cambridge Press, the book …
Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.
Calculus Revisited is a series of videos and related resources that covers …
Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.
Calculus Revisited is a series of videos and related resources that covers …
Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.
Calculus Revisited is a series of videos and related resources that covers …
Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.
Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. …
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.
Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), …
Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.
Spreadsheets Across the Curriculum activity. In advance of an actual lab activity, …
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 …
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 …
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 …
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?."
To convert between units, you're usually given one measure and asked to …
To convert between units, you're usually given one measure and asked to convert to another measure. For instance, you'll be given some volume in "gallons" and be asked to convert the volume to "fluid ounces". They will have given you (or else you can easily find) the conversion units that are suitable to the task.
The purpose of this task is to give students practice constructing functions …
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 …
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 …
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 …
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 …
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.
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