| MUET / Departments / Computer Systems & Software Engineering / Course of CS / Applied Calculus |  |
APPLIED CALCULUS
INTRODUCTION OF FUNCTIONS Mathematical and physical meaning of functions, graphs of various functions, Hyperbolic functions. INTRODUCTION TO LIMITS Theorems of limits and their applications to functions, Some useful limits, right hand and left hand limits, Continuous and discontinuous functions and their applications. DERIVATIES Introduction to derivatives, Geometrical and physical meaning of derivatives. Partial derivatives and their geometrical significance. Application problems (rate of change, marginal analysis) HIGHER DERIVATIES Leibnitz theorem, Rolles theorem, Mean value theorem. Taylors and Maclaurins series. EVALUATION OF LIMITS USING L’HOSPITAL’S RULE Indeterminate forms (0/0), (¥/¥), (o x ¥), (¥ - ¥), 1¥, ¥o, 0o APPLICATIONS OF DERIVATIES Asympototes, tangents and normals, curvature and radius of curvature, maxima and minima of a function of single variable (applied problems), differentials with application APPLICATIONS OF PARTIAL DERIVATIES Euler’s theorem, total differentials, maxima and minima of two variables INTEGRAL CALCULUS Methods of integration by substitutions and by parts. Integration of rational and irrational algebraic functions. Definite integrals, improper integrals. Gamma and Beta functions reduction formulae APPLICATIONS OF INTEGRAL CALCULUS Cost function from marginal cost, rocket flights, area under curve VECTOR ALGEBRA Introduction to vectors. Scalar and vector product of three and four vectors. Volume of paralleloppiped and tetrahedron. VECTOR CALCULUS Vector differentiation, vector integration and their applications. Ñ operator, gradient, divergence and curl with their applications. RECOMMENDED BOOKS: [1] Doniel D.Benice, "Brief Calculus and its Applications" [2] Raymond A. Barnett, "Applied Calculus" [3] Gerald L. Bradley, "Calculus" [4] Dr. S. M. Yusuf, “Calculus and Analytical Geometry”
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