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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This introductory calculus course covers differentiation and integration of functions of one variable, with applications.
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Tag(s):
- mathematics
- differentiation and integration of functions of one variable
- limits
- continuity
- differentiation rules
- extremum problems
- definite and indefinite integration
- fundamental theorem of calculus
- elementary
- techniques of integration
- approximation of definite integrals
- improper integrals
- l'h?pital's rule
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This introductory calculus course covers differentiation and integration of functions of one variable, with applications.
Author(s):
Tag(s):
- mathematics
- differentiation and integration of functions of one variable
- limits
- continuity
- differentiation rules
- extremum problems
- definite and indefinite integration
- fundamental theorem of calculus
- elementary
- techniques of integration
- approximation of definite integrals
- improper integrals
- l'h?pital's rule
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus.
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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18.014, 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.
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Tag(s):
- mathematics
- axioms for the real numbers
- the riemann integral
- limits
- theorems on continuous functions
- derivatives of functions of one variable
- the fundamental theorems of calculus
- taylor's theorem
- infinite series
- power series
- rigorous treatment of the elementary functions
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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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.
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Tag(s):
- mathematics
- differentiation of functions
- integration of functions
- limits
- continuity
- differentiation rules
- extremum problems
- definite integration
- indefinite integration
- fundamental theorem of calculus
- techniques of integration
- approximation of definite integrals
- improper integrals
- l'hôpital's rule
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover th
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Tag(s):
- mathematics
- calculus
- calculus of several variables
- vector algebra
- determinants
- matrix
- matrices
- vector-valued function
- space motion
- scalar function
- partial differentiation
- gradient
- optimization techniques
- double integrals
- line integrals
- exact differential
- conservative fields
- green's theorem
- triple integrals
- surface integrals
- divergenc
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.
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Tag(s):
- mathematics
- calculus
- calculus of several variables
- vector algebra
- determinants
- matrix
- matrices
- vector-valued function
- space motion
- scalar function
- partial differentiation
- gradient
- optimization techniques
- double integrals
- line integrals
- exact differential
- conservative fields
- green's theorem
- triple integrals
- surface integrals
- divergenc
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
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Tag(s):
- mathematics
- vector algebra
- determinant
- matrix
- matrices
- vector-valued functions
- space motion
- scalar functions
- partial differentiation
- gradient
- optimization techniques
- double integrals
- line integrals
- exact differentials
- conservative fields
- green's theorem
- triple integrals
- surface integrals
- divergence theorem
- stokes' theorem
- geometry
- v
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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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.
Author(s):
Tag(s):
- mathematics
- linear algebra
- vector integral calculus
- calculus of several variables
- vector algebra in 3-space
- determinants
- matrices
- vector-valued functions of one variable
- space motion
- scalar functions of several variables
- partial differentiation
- gradient
- optimization techniques
- double integrals and line integrals in the plane
- exact differen
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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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.
Author(s):
Tag(s):
- mathematics
- calculus
- calculus of several variables
- vector algebra
- determinants
- matrix
- matrices
- vector-valued function
- space motion
- scalar function
- partial differentiation
- gradient
- optimization techniques
- double integrals
- line integrals
- exact differential
- conservative fields
- green's theorem
- triple integrals
- surface integrals
- divergenc
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
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Tag(s):
- mathematics
- ordinary differential equations
- ode
- modeling physical systems
- first-order ode's
- linear ode's
- second order ode's
- second order ode's with constant coefficients
- undetermined coefficients
- variation of parameters
- sinusoidal signals
- exponential signals
- oscillations
- damping
- resonance
- complex numbers and exponentials
- fourier series
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.
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Tag(s):
- mathematics
- first order equations
- separation
- initial value problems
- systems
- linear equations
- independence of solutions
- undetermined coefficients
- singular points
- periodic orbits for planar systems
- first order ode's
- second order ode's
- fourier series
- laplace transform
- linear systems
- nonlinear systems
- constant coefficients
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems.
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Tag(s):
- mathematics
- quadrature
- maximum principle
- laplace transform
- existence theory
- autonomous system
- lyapunov
- limit cycles
- fourier series
- boundary value problems
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course explored topics such as complex algebra and functions, analyticity, contour integration, Cauchy's theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals, multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms.
Author(s):
Tag(s):
- mathematics
- complex algebra and functions
- analyticity
- contour integration
- cauchy's theorem
- singularities
- taylor and laurent series
- residues
- evaluation of integrals
- multivalued functions
- potential theory in two dimensions
- fourier analysis and laplace transforms.
- fourier analysis and laplace transforms
116 results found.
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