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.

Opportunity for group study by graduate students on current topics related to management not otherwise included in curriculum.

Submitted as part of the California Learning Resource Network (CLRN) Phase 3 Digital Textbook Initiative (CA DTI3), CK-12 Foundation’s Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course.

CK-12 Single Variable Calculus delivers a well-integrated course for the college-bound high school student covering advanced placement topics of functions, limits, and continuity; derivatives and applications of derivatives; integration and applications of definite integrals; transcendental functions; integration techniques; and infinite series.

This digital textbook was reviewed for its alignment with California content standards.

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.

This contemporary calculus course is the third in a three-part sequence. In this course students continue to explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.

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This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.

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CK-12's Texas Instrument Calculus Student Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

This book introduces differentiability as a local property without using limits. The philosophy behind this idea is that limits are the a big stumbling block for most students who see calculus for the first time, and they take up a substantial part of the first semester.

This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits.

This digital textbook was reviewed for its alignment with California content standards.

Introduction to investments and corporate finance. Topics include: project and company valuation, risk and return in capital markets, the pricing of stocks and bonds, corporate financing and dividend policy, the cost of capital, and financial options. Subject provides a broad overview of both theory and practice. Restricted to Management of Technology students. Financial Management studies corporate finance and capital markets, emphasizing the financial aspects of managerial decisions. It touches on all areas of finance, including the valuation of real and financial assets, risk management and financial derivatives, the trade-off between risk and expected return, and corporate financing and dividend policy. The course draws heavily on empirical research to help guide managerial decisions.

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The videos were created by renowned mathematics professor Gilbert Strang who has taught at MIT since 1962.

The video series reviews the key topics and ideas of calculus with applications to real-life situations and problems
and then fully covers the concept of Derivatives.

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. Upon successful completion of this course, the student will be able to: State the heat, wave, Laplace, and Poisson equations and explain their physical origins; Define harmonic functions; State and justify the maximum principle for harmonic functions; State the mean value property for harmonic functions; Define linear operators and identify linear operations; Identify and classify linear PDEs; Identify homogeneous PDEs and evolution equations; Relate solving homogeneous linear PDEs to finding kernels of linear operators; Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed); Explain physical significance of boundary conditions; Show uniqueness of solutions to the heat, wave, Laplace and Poisson equations with various boundary conditions; Define well-posedness; Define, characterize, and use inner products; Define the space of L2 functions, state its key properties, and identify L2 functions; Define orthogonality and orthonormal basis and show the orthogonality of certain trigonometric functions; Distinguish between pointwise, uniform, and L2 convergence and show convergence of Fourier series; Define Fourier series on [0,pi] and [0,L] and identify sufficient conditions for their convergence and uniqueness; Compute Fourier coefficients and construct Fourier series; Use the method of characteristics to solve linear and nonlinear first-order wave equations; Solve the one-dimensional wave equation using d'Alembert's formula; Use similarity methods to solve PDEs; Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions; Define the delta function and apply ideas from calculus and Fourier series to generalized functions; Derive Green's representation formula; Use Green's functions to solve the Poisson equation on the unit disk; Define the Fourier transform; Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative; Show that the inverse Fourier transform of a product is a convolution; Compute Fourier transforms of functions; Use the Fourier transform to solve the heat and wave equations on unbounded domains. (Mathematics 222)

This general math site offers reference material on a host of math topics, plus a math message board and links to relevant material online. The tables cover a range of math skills, from basic fraction-decimal conversion to the more advanced calculus and discrete math. The information is presented in notation form, with diagrams, graphs, and tables. The site is available in English, Spanish, and French. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

A basic introduction to Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive calculus course, but rather an introduction to the fundamental concepts. The third and fourth weeks introduce some basic linear algebra: vector spaces, linear transformations, matrices, matrix operations, and diagonalization. The emphasis will be on using the results, not on their proofs.

This is a textbook for a course in multivariable calculus that has been used for the past few years at Georgia Tech.

Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions. This course begins with a fresh look at limits and continuity, moves to derivatives and the process of generalizing them to higher dimensions, and finally examines multiple integrals (integration over regions of space as opposed to intervals). Upon successful completion of this course, the student will be able to: Define and identify vectors; Define and compute dot and cross-products; Solve problems involving the geometry of lines, curves, planes, and surfaces in space; Define and compute velocity and acceleration in space; Define and solve Kepler's Second Law; Define and compute partial derivatives; Define and determine tangent planes and level curves; Define and compute least squares; Define and determine boundaries and infinity; Define and determine differentials and the directional derivative; Define and compute the gradient and the directional derivative; Define, determine, and apply Lagrange multipliers to solve problems; Define and compute partial differential equations; Define and evaluate double integrals; Use rectangular coordinates to solve problems in multivariable calculus; Use polar coordinates to solve problems in multivariable calculus; Use change of variables to evaluate integrals; Define and use vector fields and line integrals to solve problems in multivariable calculus; Define and verify conservative fields and path independence; Define and determine gradient fields and potential functions; Use Green's Theorem to evaluate and solve problems in multivariable calculus; Define flux; Define and evaluate triple integrals; Define and use rectangular coordinates in space; Define and use cylindrical coordinates; Define and use spherical coordinates; Define and correctly manipulate vector fields in space; Evaluate surface integrals and relate them to flux; Use the Divergence Theorem (Gauss' Theorem) to solve problems in multivariable calculus; Define and evaluate line integrals in space; Apply Stokes' Theorem to solve problems in multivariable calculus; Properly apply Maxwell's Equations to solve problems. (Mathematics 103)

" This is a course in how corporations make use of the insights and tools of risk management. Most courses on derivatives, futures and options, and financial engineering are taught from the viewpoint of investment bankers and traders in the securities. This course is taught from the point of view of the manufacturing corporation, the utility, the software firm—any potential end-user of derivatives, but not the dealer. Most related courses focus on the extensive taxonomy of instruments and the complex models developed to price them, and on ways to exploit mispricing. While this course will make use of some of these pricing models, the focus is on how corporations use the insights and models to improve their operations, to increase the value of their real assets, or to create the financial flexibility necessary to implement their core strategy."