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Notes of Calculus with Analytic Geometry

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Notes of the Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore. This is the one of books popular for BS and BSc mathematics.

Notes of chapter 1 is written by Prof. Muhammad Farooq, notes of chapter 5 is written by Abrar Mustafa and notes of chapter 6 and 7 are written by Mr. Shahid Javed.

We will try our best to add solutions of more chapters as we are able to manage. If you have some notes which you thing are worth to share with other then please contact us from here or email at Admin [at] MathCity [dot] org.

List of chapters

Graphical interpertation of  mean value theorem
  • Rolle's theorem
  • Geometrical interpretation of Rolle's theorem
  • The mean vlaue theorem
  • Another form of mean value theorem
  • Increasing and decreasing functions
  • Cauchy's mean value theorem
  • Extended mean value theorem
  • Indeterminate form
  • The form $\frac{0}{0}$
  • The form $\frac{\infty}{\infty}$
  • The form $0\times \infty$ (or $\infty \times 0$)
  • The form $\infty-\infty$
  • The forms $0^\infty, 1^\infty, \infty^0$
  • Use of expansions

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ARW Exercise 3.1 Download PDF (1.16 MiB, 30270 downloads) View Online
ARW Exercise 3.2 Download PDF (772.51 KiB, 20653 downloads) View Online
ARW Exercise 3.3 Download PDF (2.59 MiB, 17168 downloads) View Online
ARW Exercise 3.3 by Muhammad Idrees Download PDF (695.19 KiB, 16432 downloads) View Online

We are very thankful to Muhammad Idrees for providing notes of Exercise 3.3

Cooridnate system
  • Distance between two points
  • Point divining a line segment in a given ratio
  • Straight line in $\mathbb{R}^3$
  • Direction angles of a vector
  • Angle between the straight line
  • Distance of a point from a line
  • Equations for planes
  • Angle between two planes
  • Straight line as intersection of two planes
  • Shortest distance between two straight lines
  • Cylindrical coordinates
  • Spherical coordinates
  • Surfaces
  • Surface of revolution
  • The cylinder
  • Right cylinder
  • The cone
  • The sphere
  • The ellipsoid
  • The elliptic paraboloid
  • The hyperboloid paraboloid
  • The elliptic cone
  • General quadric surfaces
  • Ruled surfaces
  • Spherical trigonometry
  • The cosine formula
  • The sine formula
  • The four parts (or the cotangent) formula
  • Latitude and longitude
  • Direction of Qibla

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ARW Exercise 8.1 Download PDF (613.14 KiB, 4869 downloads) View Online
ARW Exercise 8.2 Download PDF (1.19 MiB, 20954 downloads) View Online
ARW Exercise 8.3 Download PDF (715.33 KiB, 14509 downloads) View Online
ARW Exercise 8.4 Download PDF (668.08 KiB, 15619 downloads) View Online
ARW Exercise 8.5 Download PDF (321.66 KiB, 10585 downloads) View Online
ARW Exercise 8.6 Download PDF (578.99 KiB, 6767 downloads) View Online
ARW Exercise 8.7 Download PDF (488.29 KiB, 13103 downloads) View Online
ARW Exercise 8.8 Download PDF (105.69 KiB, 9545 downloads) View Online
ARW Exercise 8.9 Download PDF (290.39 KiB, 7753 downloads) View Online
ARW Exercise 8.10 Download PDF (678.58 KiB, 11738 downloads) View Online
ARW Direction of Qibla Download PDF (859.73 KiB, 10009 downloads) View Online
  • Homogeneous Functions
  • Differentials
  • Change of variables, the chain rule
  • Implicit functions
  • Directional derivative
  • Tangent planes and normal lines
  • Extrema of functions of two variables
  • Extrema with constraints
  • Volume of solid of revolution
  • Disc method
  • Washer method
  • Shell method
  • Cross-sectional method
  • Area of a surface of revolution
  • Volume and area in polar coordinates

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ARW Exercise 9.1 Download PDF (552.13 KiB, 16227 downloads) View Online
ARW Exercise 9.2 Download PDF (326.7 KiB, 12205 downloads) View Online
ARW Exercise 9.3 Download PDF (363.93 KiB, 12911 downloads) View Online
ARW Exercise 9.4 Download PDF (242.15 KiB, 11897 downloads) View Online
ARW Exercise 9.5 Download PDF (591.9 KiB, 12999 downloads) View Online
ARW Exercise 9.6 Download PDF (975.13 KiB, 16516 downloads) View Online
ARW Exercise 9.7 Download PDF (474.89 KiB, 10354 downloads) View Online
ARW Exercise 9.8 Download PDF (643.65 KiB, 10676 downloads) View Online
ARW Exercise 9.9 NEW Download PDF (509.32 KiB, 11174 downloads) View Online


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