![]() Course ContentSeries, vectors in R^2 and R^3, real functions of several variables, complex numbers, differential equations. Calculate constrained maxima and minima using the Method of LaGrange Multipliers.Recommended background knowledgeCalculus 1 URL study guide Course ObjectiveAt the end of this course the student is able to a) determine if a series is convergent or divergent, using several tests (like the comparison test, ratio test, alternating series test) b) work with power series (find the radius of convergence, differentiate or integrate termwise) c) find the Taylor series of several functions (like exp(x), sin(x), cos(x), ln(1+x), etc) d) calculate dot products, cross products, vector projections, distances in R^3 e) calculate partial derivatives, also using the chain rule f) find extreme values of functions of two variables, with and without constraints g) compute double integrals, also using polar coordinates g) calculate with complex numbers h) solve several first- and second-order differential equations (separable equations, first-order linear equations, second-order linear equations with constant coefficients).Calculate maxima and minima of functions of several variables.Calculate partial derivatives of functions of several variables.Evaluate functions of several variables and sketch three-dimensional surfaces.Use simple integration and separation of variables to solve differential equations.Solve basic first order differential equations.Approximate integrals using numerical integration (Trapezoidal and Simpson's rules). ![]() Use the method of integration by parts to find antiderivatives and evaluate definite integrals.Techniques of Integration ? Differential Equations.Use integration to solve applications in business and economics, such as future value and consumer and producer?s surplus.Calculate the area bounded by the graph of two or more functions by using points of intersections.Calculate the area under a curve over a closed interval.Evaluate definite integrals using substitution with original and new limits of integration.Use the method of integration by substitution to determine indefinite integrals.Evaluate definite integrals using Fundamental Theorem of Calculus.Develop the concept of definite integral using Reimann Sums.Use basic integration formulas to find indefinite integrals of algebraic, exponential, and logarithmic functions. ![]() Prerequisite: Completion of MTH 261 or equivalent with a grade of C or better. This course is intended for those who will transfer to an institution requiring two semesters of applied calculus in one of these disciplines. The general purpose of this second course in Applied Calculus is to extend the study of the techniques and applications of calculus and prepare students in business, social sciences and life sciences to apply these concepts in future mathematics and degree coursework. The course outline below was developed as part of a statewide standardization process. ![]()
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