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Course Contents

Rectangular coordinate system in space, equations of lines and planes in three dimensions. Functions of several variables: Limits, continuity, derivatives of functions of several variables, increments and differentials (partial and total differentials), Euler’s theorem, chain rule, double and triple integrals. Differntial euqations of first order. Solution of variable separable, exact and homogeneous differential equations. Linear Dqs. Bernoully DEqs. Second and higher order differential equations. Homogeneous and non-homogeneous eqs. Complementary function and particular integral. Cauchy Euler differential equations.


Course Learning Outcomes

This course includes all necessary contents, which are required in the different subjects, e.g. Physics, Chemistry, Economics, Statistics at master and higher level. It is also useful in Engineering and Banking.


calculus chapter 2 exercise 2.6 Part(1) Complete

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calculus chapter 2 exercise 2.6 Part(2) Complete in Urdu S.M.Yousuf

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calculus chapter 2 exercise 2.6 Part(3)

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calculus chapter 2 exercise 2.6 Part(4)

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The complementary function and particular integral example

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The complementary function and particular integral example

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Differential equation introduction | First order differential equations

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Equations of Lines and Planes in Three Dimensions

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Direction Cosines & Direction Angles of a Vector

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Double and Triple Integrals

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The Chain Rule

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Euler's theorem for Homogeneous Function

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Method of Small Increments

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First Order Linear Differential Equations

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Bernoulli's Equation For Differential Equations

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2nd order linear homogeneous differential equations 1

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Nonhomogeneous 2nd-order differential equations

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Cauchy-Euler Differential Equations (2nd Order)

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Book Title : Mathematical Methods
Author : S.M Yousaf and Muhammad Amin
Edition : 2005
Publisher : Illmi kitab Khana Urdu Bazar Lahore.



Book Title : Calculus and Analytic Geometry
Author : C.H. Edwards and D.E. Penny
Edition : 1982, 1986, 1988).
Publisher : Prentice Hall, International Edition, 1982, 1986, 1988).



Book Title : Calculus and Analytic Geometry
Author : G.B. Thomas Jr. and R. L. Finney
Edition : 9th edition, 1994.
Publisher : Addision-Wesely Publishing company



Book Title : Calculus
Author : 3. H.Anton
Edition : 5th Edition
Publisher : John-Wiley and sons, New York



Book Title : An Introductory Course in Differential Equations
Author : K. L. Mir
Edition : 1999
Publisher : Ilmi Kitab Khan, 1999.



Book Title : A First Course in Differential Equations With Modeling Applications
Author : D. G. Zill
Edition : 9th edition, 1994.
Publisher : Brooks/Cole Publisher, New York.







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