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Course Contents

Functions of several variables. Limits, continuity, and derivatives of functions of several variables. Increments and differentials (partial and total differentials) Euler’s theorem. Chain rule. Double and triple integrals. Rectangular coordinate system in space. Direction angles. Equations of lines and planes in three dimensions. Skew lines. Shortest distance between skew lines. Cylindrical and spherical coordinates. Differntial euqations of first order. Solution of variable separable, exact and homogeneous differential equations. Linear Differential eqs. 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.


Bernoully differential equations

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Calculus (S.M.Yousuf) Chapter 2 exercise 2.6 Part 1

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Calculus (S.M.Yousuf) Chapter 2 exercise 2.6 Part 2

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Calculus (S.M Yousuf) Chapter 2- exercise 2.6 Part 3

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Calculus (S.M.Yousuf) Chapter 2 exercise 2.6 Part 4

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Increments and differentials (partial and total differentials)

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Euler's theorem

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Chain Rule

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Double and triple integrals

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Rectangular coordinate system in space

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Direction angles

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Equations of lines and planes in three dimensions

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Skew lines

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Shortest distance between skew lines

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Cylindrical and spherical coordinates.

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Differntial euqations of first order

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Solution of variable separable

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exact and homogeneous differential equations

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Linear differential equations

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Second and higher order differential equations

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Homogeneous and non-homogeneous eqs

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Complementary function and particular integral.

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Cauchy-Euler differential equations.

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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 With Analytical Geometry
Author : S.M. Yousaf
Edition : 2005
Publisher : Illmi kitab Khana Urdu Bazar Lahore.







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