Netsanet4all.files.wordpress.com



Shenzhen Foreign Language SchoolCourse NameAdvanced Math* Multi-Variable Calculus---- 1st semester** Differential Equations----After Chinese new yearContact periods5Teacher’s InfoName: Netsanet TsegawE-mail: netsanet4all@Lecture TimeDayTimeRoomMon-FriPeriod- ? ? ? ? ?2409Target GroupSenior students who either have a deep interest to excel in Math and/or who want to study any Math based field like Engineering in University.Pre-requisite(s)Earning 5 (A/A+) in AP-Calculus BCCourse descriptionThis course covers:review of Integration techniques.review of complex Numbers. -review of parametric equations and polar coordinates. -review of vectors in 2- and 3-dimensional spaces. -partial Derivatives.-Multiple Integrals. -Vector Calculus.- Green's theorem- line integral.- Stoke's theorem - surface integrals.- Divergence theorem.* Differential Equations.- First order, second order, Linear, homogeneous, non-homogeneous, exact DE and non-exact DE-Laplace Transformations.Course ObjectivesUpon the completion of this course, you will be able to:-understand vector algebra,-write equations of lines and planes in space,-sketch graphs of functions of two variables in 3-space,-evaluate partial derivatives,-find gradients and directional derivatives of a function of several variables,-use differentials for approximation,-use tangent plane approximation,-apply partial derivatives to physical problems,-evaluate multiple integrals of different functions of several variables,-apply integrals to physical problems,-understand the core theorems (Green and Stoke) of the course.- solve different types of differential equations.Week Topics Allotted Periods Homework Assessment Chapter One. Vector valued functionsDefinition and examples of vector in spaceDistance between two points, vectors algebra(dot product, projections, cross product)1.3 Lines and planes in space1.4 Introduction to vector-valued functions1.5 Calculus of vector-valued functions1.6 Change of parameter; arc length1.7 Unit, tangent, normal 1.8 CurvatureChapter-2: Limit and continuity of function of several variables2.1. Definitions and examples of real valued functions of several variables2.2 Domain and range of functions of several variables2.3 Graphs and level curves 2.4 Limit and continuityChapte-3: Differentiation of functions of several variables3.1 Partial derivatives and its geometrical interpretation3.2 Differentiability of functions of several variables3.3 The Chain rule 3.4 Implicit differentiationChapter-4:Application of partial derivatives4.1 Directional derivatives and gradient of functions of several variables4.2 Tangent planes4.3 Differentials and tangent plane approximations4.4 Extreme values4.5 Lagrange’s multiplier4.6 Taylor’s theoremChapter-5 :Multiple integrals5.1 Double integrals5.2 Double integrals in polar coordinates5.3 Surface area5.4 Triple integrals 5.5 Triple integrals in cylindrical and spherical coordinates 5.6 Change of variables in multiple integrals Chapter-6: Calculus of vector field 6.1 Vector field 6.2 The divergence and curl of a vector field 6.3 Line integrals6.4 Green’s theorem6.5 surface integral 6.6. Stoke’s Theorem6.7. Divergence TheoremText book: Larson and Edward, Multi-Variable Calculus 10th editionReferences: 1. R. Ellis and D. Gluck, Calculus with Analytic Geometry, 3rd?Edition 2. H. Anton, Calculus With Analytic Geometry, 5th EditionEdwards &Penney, Calculus with analytic geometry, 5th editionJames Stewart, Multivariable Calculus, Edition 7E Swokowski, Calculus with Analytic GeometryThomas, Calculus and Analytic Geometry, 9th EditionDifferential EquationsIntroduction to Differential Equation-Types of DE: Ordinary and Partial-Order of DE-Degree of DE-Linearity of DESolving First Order DE1st order separable odeMethod of Integrating factor methodSolving linear deBernoulli Differential Equation1st order homogeneous ode1st order exact ode1st order non-exact ode1st order linear odeSolving Second Order DE2nd order homogeneous odeGeneral solution to HSOLDE with constant coefficients-3 casesNon-constant coefficients, HSOLDEEuler-Cauchy Equation-3 casesModeling de2nd order non-homogeneous odeMethod of Undetermined CoefficientsVariation of ParametersHigher order ode Transforms3 different types of transforms: Laplace-transforms, Fourier-transforms and Z-transformsLaplace transforms6. Partial DEPde (heat/wave/Laplace’s equation)Series solutionsAssessment Homework and Class participation ….……10% Quizzes & Tests …….50% Final Exam …… .30%Project work ……………10%Total………………………………………… ……………………….100%Wechat group: ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download