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  • Calculus
Calculus with Theory, Fall 2010
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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.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Breiner, Christine
Date Added:
01/01/2010
Engineering Mechanics II, Spring 2006
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CC BY-NC-SA
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This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from Calculus and Differential Equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.

Subject:
Calculus
Environmental Science
Life Science
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Madsen, Ole
Date Added:
01/01/2006
Geometry and Quantum Field Theory, Fall 2002
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CC BY-NC-SA
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A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.

Subject:
Calculus
Geometry
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Etingof, Pavel I.
Date Added:
01/01/2002
Hippocampus
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CC BY-NC
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HippoCampus is a project of the Monterey Institute for Technology and Education (MITE). The goal of HippoCampus is to provide high-quality, multimedia content on general education subjects to high school and college students free of charge. HippoCampus was designed as part of Open Education Resources (OER), a worldwide effort to improve access to quality education for everyone.

Subject:
Algebra
Calculus
Mathematics
Physical Science
Physics
Material Type:
Activity/Lab
Full Course
Lesson Plan
Provider:
Monterey Institute for Technology and Education (MITE)
Provider Set:
Hippocampus (MITE)
Date Added:
10/13/2017
History and Philosophy of Mechanics: Newton's Principia Mathematica, Fall 2011
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CC BY-NC-SA
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This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts.

Subject:
Calculus
Fine Arts
Mathematics
Philosophy
Social Studies
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Adam Schulman
Date Added:
01/01/2011
Introduction to Analysis, Fall 2012
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CC BY-NC-SA
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Analysis I in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Arthur Mattuck
Date Added:
01/01/2012
Mathematics for Materials Scientists and Engineers, Fall 2005
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CC BY-NC-SA
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This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Carter, W. Craig
Date Added:
01/01/2005
Multivariable Calculus, Fall 2010
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CC BY-NC-SA
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This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Auroux, Denis
Date Added:
01/01/2010
Multivariable Calculus with Theory, Spring 2011
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CC BY-NC-SA
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This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Breiner, Christine
Date Added:
01/01/2011
Numerical Computation for Mechanical Engineers, Fall 2012
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CC BY-NC-SA
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This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

Subject:
Business and Information Technology
Calculus
Career and Technical Education
Mathematics
Statistics and Probability
Technology and Engineering
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Anthony Patera
Daniel Frey
Nicholas Hadjiconstantinou
Date Added:
01/01/2012
Numerical Marine Hydrodynamics (13.024), Spring 2003
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CC BY-NC-SA
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Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Prof. Jerome Milgram
Date Added:
01/01/2003
Open Educational Resources (OER) - Calculus 1 Instructional Package
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CC BY-SA
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This Calculus I instructional package includes ancillary materials to accompany the OER Textbook Calculus Volume 1.

Subject:
Calculus
Mathematics
Material Type:
Activity/Lab
Assessment
Diagram/Illustration
Full Course
Homework/Assignment
Lecture
Lecture Notes
Lesson Plan
Module
Syllabus
Author:
Kelly Konrath
Date Added:
05/03/2024
Precalculus 1 & 2 with Trigonometry
Unrestricted Use
CC BY
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Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.

Subject:
Calculus
Mathematics
Trigonometry
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
David Lippman
Melonie Rasmussen
Date Added:
10/13/2017
Single Variable Calculus, Fall 2010
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CC BY-NC-SA
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This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Subject:
Calculus
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Jerison, David
Date Added:
01/01/2010
Single-Variable Calculus I
Unrestricted Use
CC BY
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This course is designed to introduce the student to the study of Calculus through concrete applications. Upon successful completion of this course, students will be able to: Define and identify functions; Define and identify the domain, range, and graph of a function; Define and identify one-to-one, onto, and linear functions; Analyze and graph transformations of functions, such as shifts and dilations, and compositions of functions; Characterize, compute, and graph inverse functions; Graph and describe exponential and logarithmic functions; Define and calculate limits and one-sided limits; Identify vertical asymptotes; Define continuity and determine whether a function is continuous; State and apply the Intermediate Value Theorem; State the Squeeze Theorem and use it to calculate limits; Calculate limits at infinity and identify horizontal asymptotes; Calculate limits of rational and radical functions; State the epsilon-delta definition of a limit and use it in simple situations to show a limit exists; Draw a diagram to explain the tangent-line problem; State several different versions of the limit definition of the derivative, and use multiple notations for the derivative; Understand the derivative as a rate of change, and give some examples of its application, such as velocity; Calculate simple derivatives using the limit definition; Use the power, product, quotient, and chain rules to calculate derivatives; Use implicit differentiation to find derivatives; Find derivatives of inverse functions; Find derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions; Solve problems involving rectilinear motion using derivatives; Solve problems involving related rates; Define local and absolute extrema; Use critical points to find local extrema; Use the first and second derivative tests to find intervals of increase and decrease and to find information about concavity and inflection points; Sketch functions using information from the first and second derivative tests; Use the first and second derivative tests to solve optimization (maximum/minimum value) problems; State and apply Rolle's Theorem and the Mean Value Theorem; Explain the meaning of linear approximations and differentials with a sketch; Use linear approximation to solve problems in applications; State and apply L'Hopital's Rule for indeterminate forms; Explain Newton's method using an illustration; Execute several steps of Newton's method and use it to approximate solutions to a root-finding problem; Define antiderivatives and the indefinite integral; State the properties of the indefinite integral; Relate the definite integral to the initial value problem and the area problem; Set up and calculate a Riemann sum; Estimate the area under a curve numerically using the Midpoint Rule; State the Fundamental Theorem of Calculus and use it to calculate definite integrals; State and apply basic properties of the definite integral; Use substitution to compute definite integrals. (Mathematics 101; See also: Biology 103, Chemistry 003, Computer Science 103, Economics 103, Mechanical Engineering 001)

Subject:
Calculus
Mathematics
Material Type:
Assessment
Full Course
Homework/Assignment
Reading
Syllabus
Textbook
Provider:
The Saylor Foundation
Date Added:
10/13/2017