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Transfer credit
In addition to this form, please e-mail or send to the math transfer credit examiner a Request for Additional Credit form from one of the links below and supporting materials to verify every answer on both this form and the Request for Additional Credit form. The supporting materials should include a copy of the transcript or other grade confirmation, syllabus, and exams. Please indicate relevant topics on the supporting materials. Alternatively course instructors may e-mail the examiner to support your responses.
Incoming Freshman:
http://mit.edu/firstyear/2019/subjects/incomingcredit/transfer/creditform.pdf
Incoming Transfer Student:
http://mit.edu/firstyear/transfer/credit/creditform.pdf
Continuing Student:
http://web.mit.edu/registrar/forms/reg/addcredit.pdf
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Which courses will you use to obtain transfer credit for 18.01-18.06?
For each course please list the university, number, term, instructor, textbook, and chapters. If the course has a website, then please include the link.
Your answer
Name:
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MIT ID:
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18.01: Which of the following topics were on proctored exams in your courses?
Differentiating functions using both the limit definition and rules of differentiation
Sketching the graph of a function using asymptotes, critical points, and the derivative test for increasing/decreasing and concavity properties
Setting up max/min problems and use differentiation to solve them
Setting up related rates problems and using differentiation to solve them
Evaluating integrals by using the Fundamental Theorem of Calculus
Applying integration to compute areas and volumes by slicing, volumes of revolution, arclength, and surface areas of revolution
Separation of variables for first order differential equations
L'Hospital's rule
Convergence/divergence of improper integrals, evaluating convergent improper integrals
Estimating and comparing series and integrals to determine convergence
Taylor series expansion of a function near a point, with emphasis on the first two or three terms
Integration by substitution or inverse substitution
Integration by partial fractions
Integration by parts
18.02: Which of the following topics were on proctored exams in your courses?
Put systems of linear equations in matrix format and solve them using matrix multiplication and the matrix inverse
Parametric curves as a trajectory described by a position vector, find parametric equations of a curve and compute its velocity and acceleration vectors
The gradient, including its relationship to level curves (or surfaces), directional derivatives, and linear approximation
Compute derivatives using the chain rule or total differentials
Set up and solve optimization problems involving several variables, with or without constraints
Set up and compute multiple integrals in rectangular, polar, cylindrical and spherical coordinates
Change variables in multiple integrals
Line integrals for work and flux
Surface integrals for flux
General surface integrals and volume integrals
Physical interpretation of line, surface, and volume integrals
Green's theorem
Stokes' theorem
Gauss' theorem
Physical applications of the theorems
Vector proofs
Describe geometric properties in pictures, words, vectors, and coordinates
18.03: Which of the following topics were tested on proctored exams in your courses?
Multiply two matrices.
Solving linear algebraic equations by row reduction.
Find a basis for the column space of a matrix.
Orthogonal matrices.
Symmetric matrices.
Find resonance or practical resonance frequencies for LTI differential equations.
Model RLC Circuits using LTI differential equations.
Model Spring/mass/dashpot systems using LTI differential equations.
Use operator notation P(D) when working with constant coefficient ODEs.
Compute Fourier series in terms of complex exponentials.
Modeling simple physical systems using linear ODE of first or higher order.
Employ “input signal/system response” terminology.
Solve a first order linear ODE by variation of parameters or by finding an integrating factor.
Calculate complex numbers and exponentials: Euler's formula, sinusoidal functions, and damped sinusoids.
Find the general solution of a homogeneous constant coefficient linear equations using roots of the characteristic polynomial.
Determine the stability of solutions of homogeneous constant coefficient linear equations.
Determine the oscillatory modes of solutions of homogeneous constant coefficient linear equations, and in the second order case, determine damping characteristics.
Find a particular solution of a constant coefficient linear (“LTI”) equation with driving term exponential times sinusoidal times polynomial using the Exponential Response Formula, variation of parameters, and undetermined coefficients.
Use superposition to describe the general solution of an LTI equation.
Employ the principle of time invariance to derive new solutions from old ones for an LTI equation.
Determine the amplitude gain and phase shift of the system response of an LTI system to a sinusoidal input signal using complex gain.
Determine whether a set of vectors is linearly independent
Determine whether a set of vectors spans a subspace of Euclidean space.
Determine whether a set of functions spans a subspace of a space of functions
Find the dimension of a subspace of a vector space.
Find a basis of a subspace of a vector space.
Find the coefficients of a vector with respect to a basis.
Compute the rank of a matrix.
24. Find a basis for the null-space of a matrix by row reduction.
Find the inverse and the determinant of a square matrix.
Compute and geometrically interpret the eigenvalues and eigenvectors of a square matrix.
Diagonalize a matrix.
Decouple a homogeneous linear system of constant coefficient ODEs using diagonalization.
Find normal modes of coupled oscillators.
Sketch and interpret phase portraits of second order linear systems of ODEs.
Determine phase portrait classification of a two-dimensional system from the trace and determinant.
Rewrite an nth order ODE as system of n first order ODEs using the companion matrix.
Compute matrix exponentials and express solutions of first order linear systems in terms of them using variation of parameters.
Determine Fourier series for periodic functions.
Use Fourier series to find periodic solutions of linear ODEs.
Find sine and cosine series for functions defined on an interval.
Recognize and interpret PDEs describing the one-dimensional heat and wave equations.
Solve the heat equation by separation of variables for standard boundary conditions.
Solve the wave equation using Fourier series.
Visualize solutions of first order ODEs using direction fields and isoclines; approximate them using funnels.
Employ Euler's method to estimate values of solutions of differential equations.
Determine the qualitative behavior of a nonlinear autonomous equation using the phase line and bifurcation diagrams.
Determine the qualitative behavior of higher-dimensional autonomous systems of ODEs by linearizing near critical points.
18.04: Which of the following topics were on proctored exams in your courses?
Simple Mappings
Conformality
Complex Exponential
Complex Trigonometric and Hyperbolic Functions
Contour Integrals
Liouville's Theorem
Maximum Modulus Principle
Radius of Convergence of Taylor Series
Real Integrals From -∞ to +∞
Invariance of Laplace's Equation
Bilinear/Mobius Transformations
Complex Fourier series
Oscillating Systems
Periodic Functions
Convergence of Fourier series
Gibbs phenomenon
Laplace transform and inversion formula
Path independence
Cauchy's theorem
Cauchy's integral formula
Laurent series
Zeros, singularities, point at infinity
Residue theorem
Trigonometric integrals and Jordan's lemma
Argument principle
Rouche's theorem
Cauchy-Riemann equations
18.06: Which of the following topics were on proctored exams in your courses?
Systems of linear equations
Row reduction and echelon forms
Matrix operations, including inverses
Block matrices
Linear dependence and independence
Subspaces and bases and dimensions
Orthogonal bases and orthogonal projections
Gram-Schmidt process
Linear models and least-squares problems
Determinants and their properties
Cramer's Rule
Eigenvalues and eigenvectors
Diagonalization of a matrix
Symmetric matrices
Positive definite matrices
Similar matrices
Linear transformations
Singular Value Decomposition
18.05: Which of the following topics were on proctored exams in your courses?
Probability
Set operations
Properties of probability
Finite sample spaces
Combinatorics
Multinomial coefficients
Union of events
Matching problem
Conditional probability
Independence of events
Bayes formula
Random variables and distribution
Cumulative distribution function
Marginal distributions
Conditional distributions
Multivariate distributions
Functions of random variables: Sum, Product, Ratio, Maximum, Change of Variables
Convolution
Linear Transformations of Random Vectors
Expectation
Variance
Standard deviation
Median
Law of large numbers
Chebyshev's inequality
Covariance and correlation
Cauchy-Schwartz inequality
Poisson distribution
Approximation of binomial distribution
Normal distribution
Central limit theorem
Gamma distribution
Beta distribution
Estimation theory
Bayes estimators
Maximum likelihood estimators
Chi-square distribution
t-distribution
Confidence Intervals for Parameters of Normal Distribution
Hypotheses testing
Bayes decision rules
Most Powerful Test for Two Simple Hypotheses
t-test
Two-sample t-test
Goodness-of-fit-tests
Pearson's theorem
Contingency Tables
Tests of Independence and Homogeneity
Kolmogorov-Smirnov Goodness-of-fit Test
Composite hypothesis testing
Bootstrap method
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