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  課程顧問-小管家 2023-04-25 17:12:53

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  　　同學(xué)你好，我是考而思教育的高級(jí)課程規(guī)劃Emily老師。我們有針對(duì)本預(yù)專業(yè)的預(yù)習(xí)課程。

  　　ucl預(yù)科數(shù)學(xué)覆蓋的內(nèi)容

  　　Key Topics in Mathematics

  　　A general outline of the topics that will be covered is given below.

  　　Algebraic Topics: Algebraic identities, inequalities and functions; partial fractions; quadratic equations; logarithms; remainder theorem; Pascal’s triangle; arithmetic and geometric series and their sums to n terms and sum to infinity of the convergent geometric series.

  　　Functions: Mappings; domains and ranges; exponential and log functions; inverse functions; representing a function as a curve; curve sketching and even/odd/periodic functions; finding zeros, asymptotes, symmetries, maxima and minima of function. The modulus function.

  　　Trigonometric functions and identities: Sine and cosine rules; trigonometric functions, their relationships and identities; graphical representations; periodic properties and symmetries of trigonometric functions; solution to trigonometric equations; hyperbolic functions and their identities.

  　　Calculus: To cover both differentiation and integration. Work on differentiation will include geometrical interpretation, derivatives of standard functions, differentiation of the sum, product and quotient of functions, derivatives of simple functions defined implicitly or parametrically.

  　　The derivative of the composition of two functions and its applications, along with applications to gradients, tangents, normals, maxima and minima.

  　　Work on integration will include geometric interpretation as area under a curve, the fundamental Theorem of Calculus.

  　　Also covered will be the integration of standard functions, techniques of integration, evaluation of definite integrals, evaluation of areas under a curve or between two curves, and numerical appropriations of definite integrals

  　　Vectors: Work on vectors will focus on 2D and 3D vectors, algebraic properties of addition, scalar multiplication and their geometrical properties; Distance between two points; equations of lines and planes; Direction Ratios and direction cosines; Scalar and vector products.

  　　Complex Numbers: Imaginary numbers; algebraic properties of complex numbers; complex roots of quadratic equations; argand diagrams and modulus/argument form of complex numbers; cube and nth roots of unity;

  　　DeMoivre’s theorem; exponential form of complex numbers; relationships between hyperbolic, trigonometric and exponential functions.

  　　Matrices: Column vectors; general matrix arithmetic; transformations in 2D; determinants; inverse matrices; solution to simultaneous equations; basic gaussian elimination.

  　　Numerical Applications: Numerical methods for solving integration problems: Trapezium and Simpson’s rule, small increments and rates of change; numerical solutions to algebraic functions: graphical methods, interval bisection.

  　　Differential Equations: First order differential equations and integrating factor; second order linear differential equations with constant coefficients, general solutions and particular integrals.

  　　考而思專注海外學(xué)術(shù)輔導(dǎo)13年，可以開學(xué)前預(yù)習(xí)輔導(dǎo)，開學(xué)后課件同步輔導(dǎo)、作業(yè)輔導(dǎo)、考前突擊輔導(dǎo)，學(xué)術(shù)論文輔導(dǎo)。具體的咨詢方案可以咨詢Emily老師

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