Single Variable Calculus by Prof. David Jerison of MIT

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

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Differential and Integral Calculus

This video lecture series on Differential and Integral Calculus by Professor Steve Butler provides insight into differential calculus and applications as well as an introduction to integration.

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Multivariable Calculus by Prof. Denis Auroux of MIT

This course covers vector and multi-variable calculus.Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space

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Vector Calculus

This is a series of lectures for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney.

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Differential Equations

This video lecture course on Differential Equations includes Solution of first-order ODEs by analytical, graphical and numerical methods; Linear ODEs, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams...

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The Fourier Transform and its Applications

Fourier series, the Fourier transform of continuous and discrete signals and its properties. The Dirac delta, distributions, and generalized transforms. Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems. The discrete Fourier transform and the FFT algorithm.

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Mathematical Methods for Engineers II

Difference Methods for Ordinary Differential Equations. Finite Differences, Accuracy, Stability, Convergence.One way Wave equation and CFL/ von Neumann Stability. Second order wave equation, wave profiles, heat equation / point source, Finite differences for heat equation. Convection-diffusion/ conservation laws/ analysis/ shocks. Level Set Method. Matrices in difference equations(1D, 2D, 3D). Sparse Matrices.Black-scholes equation. Iterative, General, Multigrid, Conjugate gradient and Krylov Methods. Fast Poisson solver.Weight least squares, calculus of variations/weak form. Error estimates/ projections and many more....

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Computational Science and Engineering I

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

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Numerical Analysis and Computer Programming

Programing Basics, Pointers And Arrays, External Functions and Argument Passing, Representation of Numbers, Numerical Error, Error Propagation and Stability, Polynomial Interpolation, Data Fitting, Matrix Elimation and Solution, Eigen Values, Eigen Vectors, Solving Non linear Equations, Numerical Derivations, Gaussian Rules etc...

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College Algebra

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Linear Algebra by NJ Wildberger of the University of New South Wales

This course on Linear Algebra is meant for first year undergraduates or college students. It presents the subject in a visual geometric way, with special orientation to applications and understanding of key concepts. The subject naturally sits inside affine algebraic geometry. Flexibility in choosing coordinate frameworks is essential for understanding the subject. Determinants also play an important role, and these are introduced in the context of multi-vectors in the sense of Grassmann. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.

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Linear Algebra

This course features a complete set of video lectures by Professor Gilbert Strang of MIT.This course is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. The course content includes The Geometry of Linear Equations, Elimination with Matrices, Multiplication and Inverse Matrices, Transposes, Permutations, Column Space and Nullspace, The Four Fundamental Subspaces, Orthogonal Vectors and Subspaces, Properties of Determinants, Cramer's Rule, Inverse Matrix, and Volume and lot more...

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Applied Linear Algebra and Linear Dynamical Systems

This video lecture series is an introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.......

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