Relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP Calculus curriculum.
AP Calculus AB is organized into 6 units (4 units in the first semester and 2 units in the second semester). The lessons in each unit include: Readings, Multimedia (lessons), Assignments, and Assessments. The course covers the principles of functions, derivatives, integrals, limits, approximation, and applications and modeling. Students will be able to: work with functions represented in a variety of ways; understand the connections among graphical, numerical, analytical, or verbal representations; understand the meaning of the derivative in terms of a rate of change and local linear approximation, and be able to use derivatives to solve a variety of problems; understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and use integrals to solve a variety of problems; understand the relationship between the derivative and the definite integral as expressed in both parts of the fundamental theorem of calculus.
This content is assembled from UC-approved college prep courses and is designed to acquaint students with topics in mechanics and classical electricity and magnetism. The course covers two semesters. The first semester is devoted to Newtonian mechanics, including: kinematics, laws of motion, work and energy, systems of particles, momentum, circular motion, oscillations, and gravitation. The second semester discusses the topics of electricity and magnetism. The course emphasizes problem solving including calculus, and there are numerous interactive examples throughout. You will also gain laboratory experience through interactive lab simulations and wet labs.
In physics and mathematics, series expansions to approximate functions are often used because using the exact solution is either impossible or involves unnecessary complicated calculations. This Demonstration shows accuracy for a series of expansions and how adding terms increases that accuracy moving away from the origin.
Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.
Note: this is a 57 MB PDF Document.
Atmosphere Applet: This program lets you study how the properties of the atmosphere change with altitude. You can study the atmosphere of either the Earth or Mars. The equations used in this program are taken from the ICAO standard day model for the Earth and from some curve fits of the Martian atmosphere gathered by the Global Surveyor spacecraft. Using the airplane graphic you can select an altitude, or you can type an altitude into the input box.
The program instantly outputs a selected property and displays the local temperature and pressure on gauges You can output the temperature, pressure, density, local speed of sound, Mach number for specified velocity, or the ratio of aircraft lift to the lift on Earth at sea level. Input and output can be given in either English or metric units.
This is Page 2 of a PLTL workshop for introductory physics, at the undergraduate sophomore level. It may also be used in Workshop Physics, or simply as supplemental material for the course.
Page 4 of 6 of a PLTL workshop in introductory physics, calculus-based electricity and magnetism.
Page 5 of 6 of a PLTL workshop on Coulomb law fields, for undergraduate physics.
This 9-minute video lesson gives an antidrivative example: finding öÇ(2^ln x)/x dx. [Calculus playlist: Lesson 128 of 156]
This 9-minute video lectures covers Part 1a of the 2008 BC free response. [Calculus playlist: Lesson 102 of 156]
This 10-minute video lesson looks at parts B and C of problem 1 (free response) of the AP Calculus BC Exams. [Calculus playlist: Lesson 103 of 156]
This 9-minute video lesson looks at parts C&D of problem 1 in the 2008 AP Calculus BC free response. [Calculus playlist: Lesson 104 of 156]
This 5-minute video lesson looks at part 1D of the 2008 AP Calculus BC exam (free response). [Calculus playlist: Lesson 105 of 156]
Tnis 6-minute video lesson examines finding the antiderivative using u-substitution. [Calculus playlist: Lesson 63 of 156]
This 7-minute video lesson gives a glimpse of the mystery of the Universe as we approximate e^x with an infinite series. [Calculus playlist: Lesson 95 of 156]
This 11-minute video lesson looks at parts 2B and 2C of the 2008 BC exam (free response). [Calculus playlist: Lesson 107 of 156]
This 5-minute video lesson looks at part 2D of the 2008 Calculus BC exam free-response section. [Calculus playlist: Lesson 108 of 156]
Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students.
This Internet resource provides introductory information, concept or skill development in Mathematics for grade 9, 10, 11, and 12 students who are at grade level in a single student situation. This text was initially written by David Guichard. The single variable material (not including infinite series) was originally a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.
This digital textbook was reviewed for its alignment with California content standards.
